Symmetry and decay of traveling wave solutions to the Whitham equation
arXiv:1608.07944 · doi:10.1016/j.jde.2017.01.011
Abstract
This paper is concerned with decay and symmetry properties of solitary wave solutions to a nonlocal shallow water wave model. It is shown that all supercritical solitary wave solutions are symmetric and monotone on either side of the crest. The proof is based on a priori decay estimates and the method of moving planes. Furthermore, a close relation between symmetric and traveling wave solutions is established.
References in corpus (7)
- Edge waves along a sloping beach
- The Whitham Equation as a Model for Surface Water Waves
- On the existence and stability of solitary-wave solutions to a class of evolution equations of Whitham type
- Wave breaking for the Whitham equation with fractional dispersion
- Symmetric waves are traveling waves for a shallow water equation for surface waves of moderate amplitude
- Non-uniform dependence on initial data for the Whitham equation
- Maximum principles for a fully nonlinear fractional order equation and symmetry of solutions
Cited by in corpus (10)
- Global bifurcation of solitary waves for the Whitham equation
- Symmetric waves are traveling waves for a shallow water equation for surface waves of moderate amplitude
- Solitary wave solutions to a class of Whitham-Boussinesq systems
- Symmetric solutions of evolutionary partial differential equations
- Small-amplitude fully localised solitary waves for the full-dispersion Kadomtsev--Petviashvili equation
- Solitary waves in dispersive evolution equations of Whitham type with nonlinearities of mild regularity
- Exponential decay and symmetry of solitary waves to the Degasperis-Procesi equation
- Decay of solitary waves
- Symmetry of periodic traveling waves for nonlocal dispersive equations
- The existence and decay of solitary waves for the Fornberg-Whitham equation