Abstract
We use the bifurcation method of dynamical systems to study the bifurcations of traveling wave solutions for the Kundu equation. Various explicit traveling wave solutions and their bifurcations are obtained. Via some special phase orbits, we obtain some new explicit traveling wave solutions. Our work extends some previous results.
Highlights
IntroductionWe consider the bifurcations of traveling wave solutions for the Kundu equation with the fifth-order nonlinear term: iut + uxx + c3|u|2u + c5|u|4u (1a)
In this paper, we consider the bifurcations of traveling wave solutions for the Kundu equation with the fifth-order nonlinear term: iut + uxx + c3|u|2u + c5|u|4u (1a) − is2(|u|2 u) x ir(|u|2)xu =0, x ∈ R, where c3, c5, s2, and r are real constants
By employing the bifurcation method and qualitative theory of dynamical systems, we study the bifurcations of traveling wave solutions for the Kundu equations (1a) and (1b)
Summary
We consider the bifurcations of traveling wave solutions for the Kundu equation with the fifth-order nonlinear term: iut + uxx + c3|u|2u + c5|u|4u (1a). Guo and Wu proved that the kind of solitary waves (5) for Journal of Applied Mathematics (2) is stable in [15] He and Meng [16] investigated the exact traveling waves for (4) by using the bifurcation theory and the method of phase portraits analysis. We obtain various traveling wave solutions of (1a) and (1b).
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