References
- Akers, B. and Nicholls, D. P. (2009). A stable high-order spectral method for water waves. SIAM Journal on Scientific Computing 31, 3808–3829.
- Ambrose, D. M.; Bona, J. C. and Nicholls, D. P. (2013). Global weak solutions of a model for water waves. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 469, 20130493.
- Benjamin, T. B.; Bona, J. L. and Mahony, J. J. (1972). Model Equations for Long Waves in Nonlinear Dispersive Systems. Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences 272, 47–78.
- Benjamin, T. B. and Olver, P. J. (1982). Hamiltonian structure, symmetries and conservation laws for water waves. Journal of Fluid Mechanics 125, 137–185.
- Bristeau, M.-O.; Mangeney, A.; Sainte-Marie, J. and Seguin, N. (2015). An energy-consistent depth-averaged Euler system: Derivation and properties. Discrete and Continuous Dynamical Systems - Series B 20, 961–988.
- Cheng, M.; Granero-Belinchón, R.; Shkoller, S. and Milewski, P. B. (2019). On the well-posedness of a model for capillary water waves in two dimensions. Archive for Rational Mechanics and Analysis 234, 1087–1106.
- Choi, W. (1995). Effects of Variable Depth on Boussinesq-Type Equations. Ph.D. Thesis, Kyoto University.
- Choi, W. and Camassa, R. (1999). Exact Evolution Equations for Surface Waves. Journal of Engineering Mechanics 125, 756–760.
- Cotter, C. J.; Holm, D. D. and Percival, J. R. (2010). The square root depth wave equations. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 466, 3621–3633, arXiv:https://royalsocietypublishing.org/rspa/article-pdf/466/2124/3621/784703/rspa.2010.0124.pdf.
- Craig, W. and Sulem, C. (1993). Numerical simulation of gravity waves. Journal of Computational Physics 108, 73–83.
- Dinvay, E.; Dutykh, D. and Kalisch, H. (2019). A comparative study of bi-directional Whitham systems. Applied Numerical Mathematics 141, 248–262. Nonlinear Waves: Computation and Theory-X.
- Dommermuth, D. G. and Yue, D. K. (1987). A high-order spectral method for the study of nonlinear gravity waves. Journal of Fluid Mechanics 184, 267–288.
- Duchêne, D. and Melinand, A. (2022). On well-posedness of a weakly nonlinear model for capillary–gravity waves, arXiv preprint, arXiv:2203.03277 [math.AP].
- Duchêne, V. (2022). Many Models for Water Waves.
- Duchêne, V.; Israwi, S. and Talhouk, R. (2015). A New Fully Justified Asymptotic Model for the Propagation of Internal Waves in the Camassa–Holm Regime. SIAM Journal on Mathematical Analysis 47, 240–290.
- Dyachenko, A.; Kuznetsov, E.; Spector, M. and Zakharov, V. (1996). Analytical description of the free surface dynamics of an ideal fluid (canonical formalism and conformal mapping). Physics Letters A 221, 73–79.
- Escalante, E. A.; Dumbser, M. and Castro, M. J. (2019). Space–time adaptive ADER finite volume schemes for dispersive shallow water waves. Journal of Computational Physics 396, 264–290.
- Favrie, N. and Gavrilyuk, S. (2017). A compressible two-layer model with capillary effects. Nonlinearity 30, 2718–2754.
- Gavrilyuk, S.; Nkonga, B.; Shyue, K. and Truskinovsky, L. (2020). A new paradigm for the modeling of shock waves in compressible fluids. Journal of Physics A: Mathematical and Theoretical 53, 264001.
- Green, A. E. and Naghdi, P. M. (1976). A derivation of equations for wave propagation in water of variable depth. Journal of Fluid Mechanics 78, 237–246.
- Hoang, J. and Nguyen, R. (2022). Emerald: A new fully nonlinear model for internal waves. Nonlinearity 35, 6110–6149.
- Isobe, M. (1994). Time-Dependent Mild-Slope Equations for Random Waves. In: Proceedings of the 204th International Conference on Coastal Engineering.
- Korteweg, D. J. and de Vries, G. (1895). On the Change of Form of Long Waves Advancing in a Rectangular Canal, and on a New Type of Long Stationary Waves. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 39, 422–443.
- Lannes, D. (2013). The Water Waves Problem: Mathematical Analysis and Asymptotics. Mathematical Surveys and Monographs (American Mathematical Society).
- Matsuno, Y. (1992). Bore-type solitary waves on a line of constant vorticity. Physical Review Letters 69, 609–612.
- Orszag, S. A. (1971). On the Elimination of Aliasing in Finite-Difference Schemes by Filtering. Journal of the Atmospheric Sciences 28, 1074–1074.
- Richard, G. L. (2021). A Green–Naghdi model including general vorticity. European Journal of Mechanics - B/Fluids 89, 140–153.
- West, B. J.; Brueckner, K. A.; Janda, R. S.; Milder, D. M. and Milton, R. L. (1987). A new numerical method for surface hydrodynamics. Journal of Geophysical Research: Oceans 92, 11803–11824.
- Whitham, G. B. (1967). Variational Methods and Applications to Water Waves. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences 299, 6–25.
- Zakharov, V. E.; Dyachenko, A. I. and Vasilyev, A. A. (2002). Modulation instability of deep-water gravity waves: A mechanism of wave turbulence. European Physical Journal B 27, 585–590.