title: Traveling surface waves of moderate amplitude in shallow water.
abstract: We study traveling wave solutions of an equation for surface waves of moderate amplitude arising as a shallow water approximation of the Euler equations for inviscid, incompressible and homogeneous fluids. We obtain solitary waves of elevation and depression, including a family of solitary waves with compact support, where the amplitude may increase or decrease with respect to the wave speed. Our approach is based on techniques from dynamical systems and relies on a reformulation of the evolution equation as an autonomous Hamiltonian system which facilitates an explicit expression for bounded orbits in the phase plane to establish existence of the corresponding periodic and solitary traveling wave solutions.
authors.affiliation: Departament de Matemàtiques, Facultat de Ciències, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain.
authors.forename: Armengol
authors.initials: A
authors.lastname: Gasull
authors.affiliation: Departament de Matemàtiques, Facultat de Ciències, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain.
authors.forename: Anna
authors.initials: A
authors.lastname: Geyer
keywords: Compact support; Homoclinic orbit; Shallow water; Solitary waves