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BIFURCATIONS OF TRAVELING WAVE SOLUTIONS FOR THE NONLINEAR SCHR O¨DINGER EQUATION WITH FOURTH-ORDER DISPERSION AND CUBIC-QUINTIC NONLINEARITY
Yuanfen Xu
Keywords:planar dynamical system; periodic wave solution; solitary wave solution; nonlinear Schr¨odinger equation
Abstract:
      In this paper, exact traveling wave solutions for the nonlinear schr¨odinger equation with fourth-order dispersion and cubic-quintic nonlinearity are studied by using the method of dynamical systems. Under different parametric conditions, the phase portraits of the traveling wave system are given, twenty two exact parametric representations of the traveling wave solutions to the equation are obtained.