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Explicit exact periodic wave solutions and their limit forms for a long waves-short waves model
Keywords:a long waves-short waves model; periodic wave; limit form; explicit exact solution.
Abstract:
      A long waves-short waves model is studied by using the bifurcation method of dynamical system. The sufficient conditions to guarantee the existence of solitary wave, kink and anti-kink waves, and periodic wave in different regions of the parametric space are given. All possible explicit exact parametric representations of above traveling waves are presented. When the first integral varies, we also show the convergence of the periodic wave solutions, such as the periodic wave solutions converge to the solitary wave solutions, kink and anti-kink wave solutions, and periodic wave solutions, respectively.