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

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DOI: 10.4236/ajcm.2014.42010    2,342 Downloads   3,372 Views  

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.

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Wei, M. , Gan, Y. and Tang, S. (2014) Bifurcations of Travelling Wave Solutions for the B(m,n) Equation. American Journal of Computational Mathematics, 4, 104-118. doi: 10.4236/ajcm.2014.42010.

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