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On kink and anti-kink wave solutions of Schrodinger equation with distributed delay
Keywords:Nonlinear Schrodinger equation, kink and anti-kink wave, geometric singular perturbation theory, Melnikov function, distributed delay
      This paper deals with existence problem of traveling wave solutions of a class of nonlinear Schr\"{o}dinger equation having distributed delay with a strong generic kernal. By using the geometric singular perturbation theory and the Melnikov function method, we establish results of the existence of kink and anti-kink wave solutions of the nonlinear Schrodinger equation with time delay when the average delay is sufficiently small.