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- Title
Shape analysis and damped oscillatory solutions for a class of nonlinear wave equation with quintic term.
- Authors
Li, Xiang; Zhang, Wei-guo; Li, Zheng-ming
- Abstract
This paper aims at analyzing the shapes of the bounded traveling wave solutions for a class of nonlinear wave equation with a quintic term and obtaining its damped oscillatory solutions. The theory and method of planar dynamical systems are used to make a qualitative analysis to the planar dynamical system which the bounded traveling wave solutions of this equation correspond to. The shapes, existent number, and conditions are presented for all bounded traveling wave solutions. The bounded traveling wave solutions are obtained by the undetermined coefficients method according to their shapes, including exact expressions of bell and kink profile solitary wave solutions and approximate expressions of damped oscillatory solutions. For the approximate damped oscillatory solution, using the homogenization principle, its error estimate is given by establishing the integral equation, which reflects the relation between the exact and approximate solutions. It can be seen that the error is infinitesimal decreasing in the exponential form.
- Subjects
SHAPE analysis (Computational geometry); DAMPING (Mechanics); OSCILLATIONS; SET theory; NUMERICAL solutions to nonlinear wave equations; QUINTIC surfaces; MATHEMATICAL bounds; TRAVELING waves (Physics)
- Publication
Applied Mathematics & Mechanics, 2014, Vol 35, Issue 1, p117
- ISSN
0253-4827
- Publication type
Article
- DOI
10.1007/s10483-014-1777-7