Research

I work extensively in the full spectrum of applied mathematics, including aspects such as mathematical modeling, computational modeling, numerical analysis, theoretical justification, experimentation, and physical validation. My primary area of expertise lies within the area of water waves theory and the associated partial differential equations.

Within the field of mathematical modeling, I am adept at formulating mathematical representations that capture the complicated behavior of water waves. Through rigorous theoretical justification, I ensure that these models accurately reflect the underlying physical phenomena and adhere to established mathematical principles. Additionally, I have extensive experience in computational modeling, employing advanced algorithms and numerical techniques to simulate complex dynamics and provide valuable insights into their characteristics.

Numerical analysis is another crucial component of my work, where I employ mathematical techniques to analyze the accuracy, stability, and convergence properties of numerical methods. This ensures that the computational solutions obtained are reliable and consistent with the underlying mathematical framework. To validate the findings and predictions derived from mathematical and computational models, I actively engage in experimentation. By comparing numerical and laboratory experiments, I interpret the observed results, establishing a robust connection between theory and reality.

Overall, my expertise lies in the comprehensive study of various physical phenomena and the associated partial differential equations. Through my proficiency in mathematical modeling, theoretical justification, computational modeling, numerical analysis, experimentation, and physical validation, I aim to contribute significantly in the fields of natural sciences.

In my research on mathematical modeling of water waves, I have successfully derived highly accurate nonlinear and dispersive water wave equations. These equations offer a significant advancement over the conventional nondispersive shallow water wave equations, as they address crucial limitations in describing various phenomena, including the behavior of traveling waves without breaking, wave interactions with structures, and the propagation of long nonlinear wave-trains.

One of the primary aims of my work has been to establish the theoretical properties of these derived equations. I have conducted in-depth investigations into their well-posedness, ensuring that the equations possess unique and stable solutions that depend continuously on the initial and boundary conditions. By establishing the well-posedness of the equations, I provide a solid mathematical foundation for their application in practical scenarios.

Furthermore, I have explored the existence of traveling wave solutions within these nonlinear and dispersive water wave equations. Traveling wave solutions play a crucial role in understanding the propagation characteristics of water waves, and by studying their existence, I contribute to unraveling the underlying dynamics of wave phenomena. This knowledge has important implications for a wide range of fields, including coastal engineering, oceanography, and renewable energy.

Overall, my research focuses on deriving and analyzing highly accurate nonlinear and dispersive water wave equations, studying their theoretical properties, and highlighting their significance in overcoming the limitations of existing models. Through this work, I contribute to advancing our understanding of water waves and their complex behaviors, enabling more accurate predictions and informed decision-making in various fields of application.

Further reading:

1. V. Dougalis, D. Mitsotakis and J.-C. Saut, On some Boussinesq systems in two space dimensions: Theory and numerical analysis, Math. Model. Num. Anal., 41(2007), 825–854, DOI: 10.1051/m2an:2007043 (PDF)

2. V. Dougalis, D. Mitsotakis and J.-C. Saut, On initial-boundary value problems for a Boussinesq system of BBM-BBM type in a plane domain, Discrete Contin. Dyn. Syst, 23(2009), 1191–1204,  DOI:10.3934/dcds.2009.23.1191 (PDF)

3. D. Antonopoulos, V. Dougalis and D. Mitsotakis, Initial-boundary value problems for the Bona-Smith family of Boussinesq systems,  Adv. Differential Equations, 14(2009), 27–53,  1171.35457 (PDF) - Correction (PDF)

4. Boussinesq systems in two space dimensions over a variable bottom for the generation and propagation of tsunami waves, Mat. Comp. Simul., 80(2009), 860-873,  DOI:10.1016/j.matcom.2009.08.029 (PDF)

5. V. Dougalis, D. Mitsotakis and J.-C. Saut, Initial-boundary-value problems for Boussinesq systems of Bona-Smith type on a plain domain: theory and numerical analysis, J. Sci. Comput. 44(2010), 109-135, DOI: 10.1007/s10915-010-9368-z (PDF)

6. A. Duran, D. Dutykh and D. Mitsotakis, On the Galilean invariance of some dispersive wave equations, Studies in Applied Mathematics, 131(2013), 359-388, DOI: 10.1111/sapm.12015  (PDF)

7. D. Clamond, D. Dutykh and D. Mitsotakis, Conservative modified Serre-Green-Naghdi equations with improved dispersion characteristics, Commun Nonlinear Sci Numer Simulat, 45(2017) 245-257, DOI: 10.1016/j.cnsns.2016.10.009 (PDF)

8. D. Mitsotakis, D. Dutykh, A. Assylbekuly and D. Zhakebaev, On weakly singular and fully nonlinear travelling shallow capillary-gravity waves in the critical regime, Phys. Letters A. 381(2017), 1719-1726, DOI: 10.1016/j.physleta.2017.03.041 (PDF)

9. G. Khakimzyanov, D. Dutykh, Z. Fedotova and D. Mitsotakis, Dispersive shallow water wave modelling. Part I: Model derivation on a globally flat space, Commun. Comput. Phys, 23(2018), 1-29, DOI: 10.4208/cicp.OA-2016-0179a (PDF)

10. D. Clamond, D. Dutykh and D. Mitsotakis, Hamiltonian regularisation of shallow water equations with uneven bottom, J. Phys. A: Math. Theor.  52 (2019) 42LT01, DOI: 10.1088/1751-8121/ab3eb2 (PDF)

11. T. Katsaounis, D. Mitsotakis and G. Sadaka, Boussinesq-Peregrine water wave models and their numerical approximation, J. Comp. Phys. 417 (2020), 109579, DOI:10.1016/j.jcp.2020.109579 (PDF)

12. S. Israwi, H. Kalisch, T. Katsaounis and D. Mitsotakis, A regularized shallow-water waves system with slip-wall boundary conditions in a basin: Theory and numerical analysis, Nonlinearity, 35(2022), 750-786, DOI:10.1088/1361-6544/ac3c29 (PDF)

13. S. Israwi, Y. Khalifeh and D. Mitsotakis, Equations for small amplitude shallow water waves over small bathymetric variations, Proc. R. Soc. A, 479(2023),  20230191, DOI: 10.1098/rspa.2023.0191 (PDF with corrections)

14. D. Antonopoulos and D. Mitsotakis, Bona-Smith-type systems in bounded domains with slip-wall boundary conditions: Theoretical justification and a conservative numerical scheme, Journal of Scientific Computing 102(2025) DOI:10.1007/s10915-024-02742-8 (PDF)

In addition to my contributions in deriving highly accurate nonlinear and dispersive water wave equations and studying their theoretical properties, I have also studed the phenomenon called dispersive wave runup of long, nonlinear water waves. This particular aspect of my research aims to understand and analyze the behavior of waves as they approach and interact with the shore, considering the effects of wave dispersion.

To tackle this problem, I was the first to understand that studying this particular problem requires a model that exhibits vertical translation invariance, making it suitable for studying runup phenomena. By incorporating this characteristic into Peregrine's model, I ensured its applicability to runup problems, where waves propagate towards the shore and encounter varying water depths.

To validate and demonstrate the effectiveness of the model, I conducted an experiment involving two ponds situated at different elevations. The physical laws governing the behavior of waves should remain consistent in both ponds, yet the previously established equations failed to capture this consistency. Through my work, I shed light on the understanding of dispersive runup by introducing a model that accurately represents the behavior of waves in different pond scenarios, thus overcoming the limitations of previous formulations.

In addition to my work on the long wave runup, I have also worked into the field of tsunami generation and propagation. My research has focused on developing accurate and efficient simulation techniques for modeling tsunami generation using both standard methods and more advanced approaches, such as the multi-fault solution model.

In summary, my research extends beyond the derivation and theoretical analysis of water wave equations. I have specifically explored the dispersive runup of long, nonlinear waves, introducing a model that addresses vertical translation invariance and conducting experiments to validate its effectiveness. This work has enhanced our understanding of dispersive runup phenomena and provides valuable insights for coastal engineering and related fields.

Further reading:

1. D. Mitsotakis, Boussinesq systems in two space dimensions over a variable bottom for the generation and propagation of tsunami waves, Mat. Comp. Simul., 80(2009), 860-873,  DOI:10.1016/j.matcom.2009.08.029 (PDF)

2. D. Dutykh and D. Mitsotakis, On the relevance of the dam break problem in the context of nonlinear shallow water equations, Discrete Contin. Dyn. Syst., 13(2010), 799-818, DOI: 10.3934/dcdsb.2010.13.799 (PDF) 

3. D. Dutykh, C. Labart and D. Mitsotakis, Long wave runup on random beaches, Phys. Rev. Lett., 170(2011), 184504, DOI: 10.1103/PhysRevLett.107.184504 (PDF)

4. D. Dutykh, T. Katsaounis and D. Mitsotakis, Finite volume schemes for dispersive wave propagation and run-up, Journal of Computational Physics, 230(2011), 3035-3061, DOI: 10.1016/j.jcp.2011.01.003 (PDF)

5. D. Dutykh, D. Mitsotakis, L. Chubarov and Yu. Shokin, On the contribution of the horizontal sea-bed displacements into the tsunami generation process, Ocean Modeling, 56(2012), 43-56, DOI: 10.1016/j.ocemod.2012.07.002 (PDF)

6. D. Dutykh, D. Mitsotakis, F. Dias and X. Gardeil On the use of finite fault solution for tsunami generation problems, Theor. Comp. Fluid Dyn., 27(2013), 177-199, DOI: 10.1007/s00162-011-0252-8(PDF)

7. G. Khakimzyanov, N. Shokina, D. Dutykh and D. Mitsotakis, A new run-up algorithm based on local high-order analytic expansions, J. Comp. Appl. Math. 298(2016), 82-96, DOI: 10.1016/j.cam.2015.12.004 (PDF)

8. D. Dutykh, D. MItsotakis, S. Beysel and N. Shokina, Dispersive waves generated by an underwater landslide. Numerical methods for Hyperbolic Equations, Eds: Vazquez-Cendon et al., Taylor & Francis Group, London, pp. 245 - 250, 2013, (PDF)

9.  D. Dutykh, D. Mitsotakis, S. Beisel, N. Shokina, On waves generated by an underwater landslide, In Proceedings of the IV Conference "Applied Problems of the fluid mechanics, heat and mass transfer" 1-3 November 2012, Dnepropetrovsk, Ukraine, pp. 75-79, 2012

10. D. Dutykh, T. Katsaounis and D. Mitsotakis, Dispersive wave runup on non-uniform shores, Finite volumes for complex application VI - Problems & Perspectives. Springer Proceedings in Mathematics, 2011, Volume 4, Part 1, 389 - 397, (PDF)

11. A. Duran, D. Dutykh and D. Mitsotakis, Peregrine's system revisited, in Nonlinear Physics: fluid mechanics, nonlinear waves, hydrodynamic instabilities, pattern formation, N. Abcha, E. Pelinovsky, I. Mutabazi, Springer-Verlag, Heidelberg, 2018, pp. 3-43, DOI: 10.1007/978-3-319-78193-8_1 (PDF)

The study of mathematical modeling of water waves encompasses various fascinating phenomena, including the examination of undular bores. These waves, characterized by their nonlinear and dispersive nature, manifest in diverse environments such as oceans, rivers, estuaries, and even in the atmosphere. Undular bores in oceans are tidal water waves, and understanding their behavior is of great importance in wave research.

H. Peregrine, in the 1960s, derived one of the most commonly employed Boussinesq models to analyze undular bores. However, in my recent work, we have provided a precise depiction of undular bores within this model. Notably, our findings offer a highly accurate portrayal of undular bores compared to laboratory experiments, differing from those described by the KdV equation especially for high speeds.

Furthermore, I have delved into the investigation of the impact of dissipation on the shape of undular bores through experimental estimation. By quantifying and analyzing the effects of dissipation in the evolution of dispersive shock waves, I contributed to a deeper understanding of the complex interplay between wave behavior and dissipation, shedding light on the evolution of undular bores under realistic conditions.

Further reading:

1.  D. Bolbot, A.E. Tzavaras and D. Mitsotakis, Dispersive shocks in diffusive-dispersive approximations of elasticity and quantum-hydrodynamics, Quart. Appl. Math. 81(2023), 455-481, DOI: 10.1090/qam/1658   (PDF)

2. L. Brudvik-Lindner, D. Mitsotakis and A.E. Tzavaras, Oscillatory and regularized shock waves for a dissipative Peregrine-Boussinesq system  IMA Journal of Applied Mathematics, 88(2023), 602-631, DOI: 10.1093/imamat/hxad030  (PDF)

3. D. Bolbot, A. Tzavaras and D. Mitsotakis, Oscillatory and regularized shock waves for a modified Serre-Green-Naghdi system, Studies in Applied Mathematics, 153(2024), e12694, DOI:10.1111/sapm.12694 (PDF)

I have conducted extensive research not only on surface water waves but also on internal water waves, blood flow problems, and nonlinear optics. My diverse academic endeavors encompass various fields of study. 

In the domain of biomedical engineering, I have dedicated my efforts to investigating blood flow problems. One of my notable contributions involves the derivation and in-depth examination of asymptotic equations for blood flow within large arteries. By studying the behavior of blood flow in such crucial pathways, I have advanced our understanding of the intricate dynamics at play and their implications for cardiovascular health.

Moreover, my research endeavors have extended to the field of nonlinear optics, where I have focused on the interaction of long nonlinear optical waves with boundaries. I have gained valuable knowledge regarding the behavior of nonlinear optical systems in diverse settings. 

In addition, I have undertaken studies on nonlocal models for internal waves, exploring their theoretical foundations and practical implications. By delving into these nonlocal models, I have expanded our understanding of the complex dynamics underlying internal water waves, shedding light on their propagation, interactions, and potential applications in fields like oceanography and coastal engineering.

Recognizing the transformative potential of machine learning, I have applied its powerful techniques to tackle the challenging domain of ill-posed inverse water wave problems. By harnessing the capabilities of machine learning algorithms, I aim to overcome the inherent difficulties associated with these problems, where limited or noisy data hinder the accurate reconstruction of wave characteristics.

Overall, my research portfolio encompasses a wide range of topics, including surface water waves, internal water waves, blood flow problems in large arteries, nonlinear optics, and nonlocal models for internal waves. By venturing into these interdisciplinary realms, I aim to contribute to the advancement of knowledge and foster innovation in various scientific disciplines.

Further reading:

1. V. Dougalis, A. Duran and D. Mitsotakis, Numerical approximation of solitary waves of the Benjamin equation, Math. Comp. Simul. 127(2016), 56-79, DOI: 10.1016/j.matcom.2012.07.008 (PDF)

2. V. Dougalis, A. Duran and D. Mitsotakis, Numerical solution of the Benjamin equation, Wave Motion 52(2015), 194-215, DOI: 10.1016/j.wavemoti.2014.004 (PDF)

3. T. Katsaounis and D. Mitsotakis On the reflection of solitons of the cubic nonlinear Schrodinger equation, Math. Meth. Appl. Sci., 41(2018), 1013-1018, DOI: 10.1002/mma.4070(PDF)

4.  A. Duran, V. Dougalis and D. Mitsotakis, Numerical approximation to Benjamin type equations. Generation and stability of solitary waves, Wave Motion, 85(2019), 34-56, DOI: 10.1016/j.wavemoti.2018.11.002  (PDF)

5.  D. Mitsotakis, D. Dutykh, Q. Li, Asymptotic nonlinear and dispersive pulsatile flow in elastic vessels with cylindrical symmetry, Computers and Mathematics with Applications, 75(2018), 4022-4047, DOI: 10.1016/j.camwa.2018.03.011 (PDF)

6. D. Dutykh, M. Hoefer, and D. Mitsotakis, Solitary wave solutions and their interactions for fully nonlinear water waves with surface tension in the generalized Serre equations, Theor. Comp. Fluid. Dyn., 32(2018), 371-397, DOI: 10.1007/s00162-018-0455-3 (PDF)

7. D. Mitsotakis, D. Dutykh, Q. Li and E. Peach, On some model equations for pulsatile flow in viscoelastic vessels, Wave Motion 90(2019),139-151, DOI: 10.1016/k.wavmoti.2019.05.004 (PDF)

8. D. Antonopoulos, V. Dougalis and D. Mitsotakis, Error estimates for Galerkin finite element methods for the Camassa-Holm equation, Numerische Mathematik 142(2019), 833-862, DOI: 10.1007/s00211-019-01045-7 (PDF)

9. J. Bona, A. Duran and D. Mitsotakis, Solitary-wave solutions of Benjamin-Ono and other systems for internal waves. I. Approximations, Discrete Contin. Dyn. Syst. 41(2021), 87-111,  DOI: 10.3934/dcds.2020215 (PDF)

10. D. Mantzavinos and D. Mitsotakis Extended water wave systems of Boussinesq equations on a finite interval: Theory and numerical analysis, Journal de Mathématiques Pures et Appliquées, 169(2023), 109-137,  DOI: 10.1016/j.matpur.2022.11.009 (PDF)

11. A. Jagdap, D. Mitsotakis and G. Karniadakis, Deep learning of inverse water waves problems using multi-fidelity data:  Application to Serre-Green-Naghdi equations, Ocean Engineering, 248(2022), 110775, DOI:10.1016/j.oceaneng.2022.110775 (PDF)

Throughout my research, I have extensively explored and evaluated various numerical methods for modeling nonlinear and dispersive waves. Specifically, my findings regarding classical discontinuous Galerkin and finite volume methods indicate that these approaches exhibit significant dissipative behavior when attempting to accurately capture nonlinear and dispersive phenomena, particularly over extended time periods required for example in studies of transoceanic tsunamis and the interaction of long solitary waves. Additionally, deriving conservative versions of these methods has proven to be challenging, leading to substantial errors compared to continuous Galerkin methods or spectral methods.

To enhance the efficiency of these methods, I have employed the UNO2 reconstruction technique, which has demonstrated superior performance in my investigations. By implementing this reconstruction approach, I have sought to improve the accuracy and reliability of classical discontinuous Galerkin and finite volume methods for modeling nonlinear and dispersive waves.

While multisymplectic methods are known for their accuracy due to their conservation properties, I have found that they may not be suitable for solving realistic water wave problems that involve complex bathymetries. Instead, these methods appear to be more suited for idealized equations with flat bottom topographies, limiting their applicability in practical scenarios.

Among the various numerical methods, the Fourier pseudospectral method stands out as one of the most accurate for modeling dispersive waves. However, it has its limitations, as it is only applicable to periodic domains and becomes challenging to employ in cases involving variable bottom topography or significant nonlinearities.

Based on my extensive evaluations, it appears that the continuous Galerkin method emerges as the most efficient approach for solving nonlinear and dispersive equations. Notably, the Galerkin methods developed in my research are accompanied by theoretical justifications and convergence proofs, which are critical for establishing their accuracy and reliability. I have conducted comprehensive error estimations and demonstrated their well-posedness in one- and two-dimensional domains with various boundary conditions, setting them apart as the only numerical methods currently supported by rigorous theoretical analysis in this context.

It is worth noting that our Galerkin method for the Serre-Green-Naghdi equations stands out as the only method that has been proven to be convergent for the particular system. Currently, the theoretical framework has been established solely with respect to periodic boundary conditions. Moving forward, further research is required to extend the theoretical foundations of our method to encompass bounded domains. The development of a comprehensive theory for the continuous model in such domains would significantly enhance the applicability and practicality of the Galerkin method, opening up opportunities for a broader range of real-world scenarios and facilitating more accurate simulations.

In summary, my research focuses on the evaluation and improvement of numerical methods for modeling nonlinear and dispersive waves. While classical discontinuous Galerkin and finite volume methods have limitations, I have utilized UNO2 reconstruction to enhance their performance. Multisymplectic methods exhibit accuracy but may not be suitable for realistic water wave problems. Fourier pseudospectral methods are highly accurate but limited in their applicability. Ultimately, continuous Galerkin methods have shown to be the most efficient, accompanied by rigorous theoretical analysis and convergence proofs, thus establishing their effectiveness in solving nonlinear and dispersive equations.

1. On some Boussinesq systems in two space dimensions: Theory and numerical analysis,  (with V. Dougalis and J.-C. Saut), Math. Model. Num. Anal., 41(2007), 825–854, DOI: 10.1051/m2an:2007043 (PDF)

2. Numerical solution of Boussinesq systems of the Bona-Smith family. (with D. Antonopoulos and V. Dougalis), Appl. Numer. Math., 30(2010), 314-336, DOI:10.1016/j.apnum.2009.03.002 (PDF)

3. Initial-boundary-value problems for Boussinesq systems of Bona-Smith type on a plain domain: theory and numerical analysis, (with V. Dougalis and J.-C. Saut), J. Sci. Comput. 44(2010), 109-135, DOI: 10.1007/s10915-010-9368-z (PDF)

4. Galerkin approximations of periodic solutions of Boussinesq systems. (with D. Antonopoulos and V. Dougalis), Bulletin of the Greek Mathematical Society, 57(2010), 13-30, hellenic mathematical society  (PDF)

5. Finite volume schemes for dispersive wave propagation and run-up (with D. Dutykh and T. Katsaounis), Journal of Computational Physics, 230(2011), 3035-3061, DOI: 10.1016/j.jcp.2011.01.003 (PDF)

6. Finite volume methods for unidirectional dispersive wave models. (with D. Dutykh and T. Katsaounis), Int. J. Numer. Meth. Fluids, 71(2013), 717-736, DOI: 10.1002/fld.3681 (PDF)

7. Finite volume and pseudo-spectral schemes for the fully nonlinear 1D Serre equations. (with D. Dutykh, D. Clamond and P. Milewski), European J. Appl. Math., 24(2013), 761-787, DOI: http://dx.doi.org/10.1017/S0956792513000168 (PDF)

8. On the Galerkin/finite element method for the Serre equations. (with D. Dutykh and B. Ilan), J. Sci. Comp. 61(2014), 166-195, DOI: 10.1007/s10915-014-9823-3 (PDF)

9. Numerical solution of the Benjamin equation. (with V. Dougalis and A. Duran), Wave Motion 52(2015), 194-215, DOI: 10.1016/j.wavemoti.2014.004 (PDF)

10. Numerical approximation of solitary waves of the Benjamin equation. (with V. Dougalis and A. Duran), Math. Comp. Simul. 127(2016), 56-79, DOI: 10.1016/j.matcom.2012.07.008 (PDF)

11. A new run-up algorithm based on local high-order analytic expansions. (with D. Dutykh, G. Khakimzyanov and N. Shokina), J. Comp. Appl. Math. 298(2016), 82-96, DOI: 10.1016/j.cam.2015.12.004 (PDF)

12. Legendre pseudospectral approximation of Boussinesq systems and applications to wave breaking. (with M. Bjorkavag, H. Kalisch, Z. Khorsand), J. Math. Study, 49(2016), 221-237, DOI: 10.4208/jms.v49n3.16.01 (PDF)

13. A Modified Galerkin / Finite Element Method for the numerical solution of the Serre-Green-Naghdi system. (with M. McGuinness and C. Synolakis), Int. J. Numer. Meth. Fluids, 83(2017), 755-778, DOI: 10.1002/fld.4293 (PDF)

14. Error estimates for Galerkin approximations of the Serre equations. (with D. Antonopoulos and V. Dougalis), SIAM J. Numer. Anal. 55(2017), 841-868, DOI: 10.1137/16M1078355 (PDF) 

15. Numerical approximation to Benjamin type equations. Generation and stability of solitary waves (with A. Duran and V. Dougalis), Wave Motion, 85(2019), 34-56, DOI: 10.1016/j.wavemoti.2018.11.002  (PDF)

16. On the multi-symplectic structure of Boussinesq-type systems. I: Derivation and mathematical properties (with A. Duran and D. Dutykh), Physica D, 338(2019), 10-21, DOI: 10.1016/j.physd.2018.11.007 (PDF)

17. Numerical simulation of conservation laws with moving grid nodes: Application to tsunami wave modelling (with D. Dutykh, G. Khakimzyanov and N. Shokina), Geosciences 9(2019), 197, DOI: 10.3390/geosciences9050197  (PDF)

18. Error estimates for Galerkin finite element methods for the Camassa-Holm equation (with D. Antonopoulos and V. Dougalis), Numerische Mathematik 142(2019), 833-862, DOI: 10.1007/s00211-019-01045-7 (PDF)

19. On the multi-symplectic structure of Boussinesq-type systems. II: Geometric discretization (with A. Duran and D. Dutykh), Physica D 397(2019), 1-16,  DOI: 10.1016/j.physd.2019.05.002 (PDF)

20. Boussinesq-Peregrine water wave models and their numerical approximation (with Th. Katsaounis and G. Sadaka), J. Comp. Phys. 417 (2020), 109579, DOI:10.1016/j.jcp.2020.109579 (PDF)

21. A regularized shallow-water waves system with slip-wall boundary conditions in a basin: Theory and numerical analysis (with S. Israwi, H. Kalisch and T. Katsaounis) Nonlinearity, 35(2022), 750-786, DOI:10.1088/1361-6544/ac3c29 (PDF)

22. A conservative fully-discrete numerical method for the regularised shallow water wave equations (with D. Ketcheson, H. Ranocha and E. Süli) SIAM J. Sci. Comput. 43(2021), B508-B537, DOI: 10.1137/20M1364606 (PDF)

23. A broad class of conservative numerical methods for dispersive wave equations (with H. Ranocha and D. Ketcheson) Commun. Comput. Phys. 29(2021), 979-1029, DOI:10.402/cicp.OA-2020-0119 (PDF)

24. Solitary-wave solutions of Benjamin-Ono and other systems for internal waves. I. Approximations (with J. Bona and A. Duran), Discrete Contin. Dyn. Syst. 41(2021), 87-111,  DOI: 10.3934/dcds.2020215 (PDF)