Gasull Armengol, Geyer Anna
Departament de Matemàtiques, Facultat de Ciències, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain.
Nonlinear Anal Theory Methods Appl. 2014 Jun;102(100):105-119. doi: 10.1016/j.na.2014.02.005.
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.
我们研究了作为无粘性、不可压缩且均匀流体的欧拉方程浅水近似而产生的中等振幅表面波方程的行波解。我们得到了隆起和凹陷的孤立波，包括一族具有紧支集的孤立波，其中振幅可能相对于波速增加或减小。我们的方法基于动力系统技术，并依赖于将演化方程重新表述为一个自治哈密顿系统，这有助于在相平面中为有界轨道给出显式表达式，以建立相应的周期和孤立行波解的存在性。
