The Bifurcations of Traveling Wave Solutions of the Kundu Equation

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.

[1]  Boling Guo,et al.  Orbital stability of solitary waves for Kundu equation , 2009 .

[2]  V. Gerdjikov,et al.  Hierarchies of Hamiltonian structures , 2008 .

[3]  Huiqun Zhang,et al.  Various exact travelling wave solutions for Kundu equation with fifth-order nonlinear term , 2010 .

[4]  B. Guo,et al.  Orbital Stability of Solitary Waves for the Nonlinear Derivative Schrödinger Equation , 1995 .

[5]  Ming Song,et al.  New Exact Solutions for the $(2+1)$-Dimensional Broer-Kaup-Kupershmidt Equations , 2010 .

[6]  Zheng-rong Liu,et al.  Peaked wave solutions of Camassa–Holm equation , 2004 .

[7]  Hong-qing Zhang,et al.  New Exact Travelling Wave Solutions to Kundu Equation , 2005 .

[8]  Anjan Kundu,et al.  Landau-Lifshitz and higher-order nonlinear systems gauge generated from nonlinear Schrödinger-type equations , 1984 .

[9]  Susumu Takeda,et al.  Modified Nonlinear Schrödinger Equation for Alfvén Waves Propagating along the Magnetic Field in Cold Plasmas , 1975 .

[10]  R. Deissler,et al.  Generation of counterpropagating nonlinear interacting traveling waves by localized noise , 1988 .

[11]  Zhaosheng Feng,et al.  Explicit Exact Solitary Wave Solutions for the Kundu Equation and the Derivative Schrödinger Equation , 2001 .

[12]  P. C. Hohenberg,et al.  Fronts, pulses, sources and sinks in generalized complex Ginzberg-Landau equations , 1992 .

[14]  Anjan Biswas,et al.  Topological Soliton Solution and Bifurcation Analysis of the Klein-Gordon-Zakharov Equation in (1+1)-Dimensions with Power Law Nonlinearity , 2013, J. Appl. Math..

[15]  H. H. Chen,et al.  Integrability of Nonlinear Hamiltonian Systems by Inverse Scattering Method , 1979 .

[16]  Jibin Li,et al.  Smooth and non-smooth traveling waves in a nonlinearly dispersive equation , 2000 .

[17]  Bin He,et al.  Bifurcations and new exact travelling wave solutions for the Gerdjikov–Ivanov equation , 2010 .

[18]  A. Biswas 1-soliton solution of the generalized Radhakrishnan, Kundu, Lakshmanan equation , 2009 .

[19]  Zheng-rong Liu,et al.  Peakons of the Camassa–Holm equation , 2002 .

[20]  E. Mjølhus,et al.  On the modulational instability of hydromagnetic waves parallel to the magnetic field , 1976, Journal of Plasma Physics.

[21]  Boling Guo,et al.  Periodic blow-up solutions and their limit forms for the generalized Camassa–Holm equation , 2008 .