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Volume 10, Number 2, 2020, Pages 795-815                                                                DOI:10.11948/20190408
Bifurcations and exact traveling wave solutions of the equivalent complex short-pulse equations
Jinsen Zhuang,Yan Zhou
Keywords:Solitary wave solution, periodic wave solution, peakon solution, periodic peakon solution, compacton solution, equivalent complex short-pulse equation.
Abstract:
      In this paper, we study the traveling wave solutions for a complex short-pulse equation of both focusing and defocusing types, which governs the propagation of ultrashort pulses in nonlinear optical fibers. It can be viewed as an analog of the nonlinear Schrodinger (NLS) equation in the ultrashort-pulse regime. The corresponding traveling wave systems of the equivalent complex short-pulse equations are two singular planar dynamical systems with four singular straight lines. By using the method of dynamical systems, bifurcation diagrams and explicit exact parametric representations of the solutions are given, including solitary wave solution, periodic wave solution, peakon solution, periodic peakon solution and compacton solution under different parameter conditions.
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