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2008•Journal of Guilin University of Electronic TechnologyRequires access

Bifurcations of travelling wave solutions for generalized KP-BBM equation

Luo Guo

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Abstract

Using the bifurcation theory of planar dynamical systems to study the generalized KP-BBM equation,the phase portraits of the traveling wave system are given.It is pointed out that the existence of singular straight line in the traveling wave system is the factor that causes smooth periodic wave to converge periodic cusp waves.Under different parametric conditions,various sufficient conditions to guarantee the existence of the above solutions and some exact explicit parametric representations of above solutions are obtained.

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What this paper is about

Using the bifurcation theory of planar dynamical systems to study the generalized KP-BBM equation,the phase portraits of the traveling wave system are given.It is pointed out that the existence of singular straight line in the traveling wave system is the factor that causes smooth periodic wave to converge periodic cusp waves.Under different parametric conditions,various sufficient conditions to guarantee the existence of the above solutions and some exact explicit parametric representations of above solutions are obtained.

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Available abstract

Using the bifurcation theory of planar dynamical systems to study the generalized KP-BBM equation,the phase portraits of the traveling wave system are given.It is pointed out that the existence of singular straight line in the traveling wave system is the factor that causes smooth periodic wave to converge periodic cusp waves.Under different parametric conditions,various sufficient conditions to guarantee the existence of the above solutions and some exact explicit parametric representations of above solutions are obtained.

Key concepts: Phase portrait, Cusp (singularity), Mathematics, Mathematical analysis, Bifurcation, Traveling wave, Sinusoidal plane-wave solutions of the electromagnetic wave equation, Parametric statistics

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