Symmetric waves are traveling waves for a shallow water equation for surface waves of moderate amplitude

Abstract

Following a general principle introduced by Ehrnström et.al. we prove that for an equation modeling the free surface evolution of moderate amplitude waves in shallow water, all symmetric waves are traveling waves.

References in corpus (3)

• The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations
• Symmetry and decay of traveling wave solutions to the Whitham equation
• Singular solutions for a class of traveling wave equations arising in hydrodynamics

Cited by in corpus (4)

• Symmetry and decay of traveling wave solutions to the Whitham equation
• Symmetric solutions of evolutionary partial differential equations
• Well-posedness of a highly nonlinear shallow water equation on the circle
• Exponential decay and symmetry of solitary waves to the Degasperis-Procesi equation