Numerical study of a nonlocal model for water-waves with variable depth, Wave Motion, vol.50, p.7, 2013. ,
, Bidirectional Whitham equations as models of waves on shallow water, p.9, 2017.
, Numerical bifurcation and spectral stability of wavetrains in bidirectional Whitham models, vol.1, p.16, 2017.
Nonlinear evolution equations for two-dimensional surface waves in a fluid of finite depth, J. Fluid Mech, vol.295, issue.6, pp.381-394, 1995. ,
Numerical simulation of gravity waves, J. Comp. Phys, vol.108, pp.73-83, 1993. ,
Hamiltonian long-wave approximations to the water-wave problem, Wave Motion, vol.19, issue.4, pp.367-389, 1994. ,
Hamiltonian long-wave expansions for free surfaces and interfaces, Comm. Pure Appl. Math, vol.58, pp.1587-1641, 2005. ,
The Whitham equation with surface tension, Nonlinear Dyn, vol.4, p.5, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01504047
, Existence of a highest wave in a fully dispersive two-way shallow water model
The Whitham equation for hydroelastic waves ,
Traveling waves for the Whitham equation, Diff. Int. Eq, vol.22, pp.1193-1210, 2009. ,
Global bifurcation for the Whitham equation, Math. Modelling Natural Phenomena, vol.8, pp.13-30, 2013. ,
Classical well-posedness in dispersive equations with nonlinearities of mild regularity, and a composition theorem in Besov spaces, 2009. ,
A conditional well-posedness result for the bidirectional Whitham equation, p.17, 2007. ,
, Geometric Numerical Integration. Structure-Preserving Algorithms for Ordinary Differential Equations, vol.10, p.20, 2006.
URL : https://hal.archives-ouvertes.fr/hal-01403326
Modulational instability in the Whitham equation of water waves, Studies in Applied Mathematics, vol.134, pp.120-143, 2015. ,
Modulational instability in a full-dispersion shallow water model, 2016. ,
The Water Waves Problem, Mathematical Surveys and Monographs, vol.188, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-01101991
Derivation of asymptotic two-dimensional time-dependent equations for surface water wave propagation, Phys. Fluids, vol.21, 2009. ,
Remarks on the full dispersion Kadomtsev-Petviashvili equation, Kinet. Relat. Models, vol.6, pp.989-1009, 2013. ,
A Numerical Study of the Exact Evolution Equations for Surface Waves in Water of Finite Depth, Stud. Appl. Math, vol.113, issue.11, pp.303-324, 2004. ,
Dispersive perturbations of Burgers and hyperbolic equations I: local theory, SIAM J. Math. Anal, vol.46, pp.1505-1537, 2014. ,
Two-dimensional evolution of surface gravity waves on a fluid of arbitrary depth, Phys. Rev. E, vol.47, p.6, 1993. ,
The Whitham Equation as a model for surface water waves, Phys. D, vol.309, p.7, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01136855
Stability of traveling wave solutions to the Whitham equation, Phys. Lett. A, vol.378, pp.2100-2107, 2014. ,
Boussinesq long-wave model for variable topography, Wave Motion, vol.65, issue.2, pp.156-174, 2016. ,
The conformal-mapping method for surface gravity waves in the presence of variable bathymetry and mean current, Procedia IUTAM, vol.11, pp.110-118, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-00855780
Variational methods and applications to water waves, Proc. Roy. Soc. London A, vol.299, p.9, 1967. ,
Linear and Nonlinear Waves, vol.2, p.9, 1974. ,
Construction of higher order symplectic integrators, Physics Letters A, vol.150, issue.9, pp.262-268, 1990. ,
Stability of periodic waves of finite amplitude on the surface of a deep fluid, J. Appl. Mech. Tech. Phys, vol.9, pp.190-194, 1968. ,
, evgueni.dinvay@math.uib.no, henrik.kalisch@math.uib.no, Department of Mathematics, University of Bergen, vol.7800, p.5020
,