Year: 2012
Author: Xiang Li, Weiguo Zhang, Yan Zhao
Advances in Applied Mathematics and Mechanics, Vol. 4 (2012), Iss. 5 : pp. 559–574
Abstract
In this paper, we analyze the relation between the shape of the bounded traveling wave solutions and dissipation coefficient of nonlinear wave equation with cubic term by the theory and method of planar dynamical systems. Two critical values which can characterize the scale of dissipation effect are obtained. If dissipation effect is not less than a certain critical value, the traveling wave solutions appear as kink profile; while if it is less than this critical value, they appear as damped oscillatory. All expressions of bounded traveling wave solutions are presented, including exact expressions of bell and kink profile solitary wave solutions, as well as approximate expressions of damped oscillatory solutions. For approximate damped oscillatory solution, using homogenization principle, we give its error estimate by establishing the integral equation which reflects the relations between the exact and approximate solutions. It can be seen that the error is an infinitesimal decreasing in the exponential form.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.10-m11181
Advances in Applied Mathematics and Mechanics, Vol. 4 (2012), Iss. 5 : pp. 559–574
Published online: 2012-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Nonlinear wave equation planar dynamical system exact solutions approximate damped oscillatory solutions error estimate.
Author Details
-
Shape analysis and damped oscillatory solutions for a class of nonlinear wave equation with quintic term
Li, Xiang
Zhang, Wei-guo
Li, Zheng-ming
Applied Mathematics and Mechanics, Vol. 35 (2014), Iss. 1 P.117
https://doi.org/10.1007/s10483-014-1777-7 [Citations: 1]