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Bifurcations of Travelling Wave Solutions for the B(m,n) Equation
School of Information and Statistics, Guangxi University of Finance and Economics, Nanning, China
School of Information and Statistics, Guangxi University of Finance and Economics, Nanning, China
School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin, China
- 1 School of Information and Statistics, Guangxi University of Finance and Economics, Nanning, China
- 2 School of Information and Statistics, Guangxi University of Finance and Economics, Nanning, China
- 3 School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin, China
American Journal of Computational Mathematics·Volume 04 (2014)·Pages 104–118·Published 20 March 2014·DOI10.4236/ajcm.2014.42010
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Abstract
Using the bifurcation theory of dynamical systems to a class of nonlinear fourth order analogue of the B(m,n) equation, the existence of solitary wave solutions, periodic cusp wave solutions, compactons solutions, and uncountably infinite many smooth wave solutions are obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given. Some exact explicit parametric representations of the above waves are determined.
KeywordsSolitary Wave SolutionPeriodic Cusp Wave SolutionPeriodic Wave SolutionSmoothness of WaveB(mn) Equation
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