Bifurcations of Travelling Wave Solutions for the B(m,n) Equation

Minzhi Wei, Yujian Gan, Shengqiang Tang

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.

DOI: 10.4236/ajcm.2014.42010                

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.

Keywords

Solitary Wave Solution; Periodic Cusp Wave Solution; Periodic Wave Solution; Smoothness of Wave; B(m, n) Equation

Conflicts of Interest

The authors declare no conflicts of interest.

References

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