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DYNAMICAL BEHAVIOUR AND EXACT SOLUTIONS OF THIRTEENTH ORDER DERIVATIVE NONLINEAR SCHRODINGER EQUATION
Keywords:Coupled integrable system, Exact solution, Thirteenth order derivative nonlinear Schrodinger equation, Homoclinic orbits, Heteroclinic orbits, Periodic orbits.
Abstract:
      In this paper, we considered the model of the thirteenth order derivatives of nonlinear Schrodinger equations. It is shown that a wave packet ansatz inserted into these equations leads to an integrable Hamiltonian dynamical sub-system. By using bifurcation theory of planar dynamical systems, in different parametric regions, we determined the phase portraits. In each of these parametric regions we obtain possible exact explicit parametric representation of the traveling wave solutions corresponding to homoclinic, heteroclinic and periodic orbits.