Weak solutions of a generalized Boussinesq system
type: Item
instance of: scholarly article
title: Weak solutions of a generalized Boussinesq system
zbMATH Open document ID: 0941.35078
DOI: 10.1023/A:1022611428785
author: Yanyan Li
published in: Journal of Dynamics and Differential Equations
publication date: 2000-08-13T00:00:00Z
review text: The dynamical systems reduced from the unperturbed and perturbed Boussinesq equations are compared. Four types of weak solutions, including compactons, peakons, rampsons and meseons are shown to be limits of analytic solitary wave solutions of the perturbed system. The solitary wave solutions representing homoclinic orbits or heteroclinic orbits of the perturbed Boussinesq equations are extended to analytic functions defined on some strips in the complex plane, whose boundaries contain singularities as branch points of these functions. These singularities approach the real axis as the corresponding solitary wave solutions converge to any one of the analyzed weak solutions, which is an indication of the strong influence by the nonlinear dispersion terms on the formation of the nonanalytic weak solution.
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 37J45
Mathematics Subject Classification ID: 35A20
zbMATH DE Number: 1389696
zbMATH Keywords: Boussinesq systems
zbMATH Keywords: weak solutions
zbMATH Keywords: homoclinic orbits
zbMATH Keywords: traveling wave solutions
zbMATH Keywords: perturbed Boussinesq equations
reviewed by: L. Vázquez
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1389696