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Scholars Journal of Physics, Mathematics and Statistics | Volume-5 | Issue-05
Bifurcation of Traveling Wave Solutions for the Bogoyavlenskii- KadomtsevPetviashvili Equation
Feiting Fan, Yuqian Zhou
Published: Oct. 30, 2018 | 136 115
DOI: 10.21276/sjpms.2018.5.5.1
Pages: 282-290
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Abstract
This paper studies each type of traveling waves of the traveling wave system corresponding to the Bogoyavlenskii-Kadomtsev-Petviashvili equation comprehensively and systematically. By transforming its traveling wave system into a dynamical system in R3, we employ the bifurcation method of dynamical system to investigate its phase space geometry in detail. Finally, by calculating the complicated elliptic integrals, we obtain exact expressions of all traveling wave solutions of the BogoyavlenskiiKadomtsev-Petviashvili equation without any loss. Keywords: Bogoyavlenskii-Kadomtsev-Petviashvili equation, traveling wave solutions, dynamical system, bifurcation.