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Volume 7, Number 4, 2017, Pages 1503-1533                                                                DOI:10.11948/2017092
Explicit exact periodic wave solutions and their limit forms for a long waves-short waves model
Bin He,Qing Meng
Keywords:A long waves-short waves model, solitary wave solution, kink and anti-kink wave solutions, periodic wave solution, limit form.
      A long waves-short waves model is studied by using the approach of dynamical systems. 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 energy of Hamiltonian system corresponding to this model 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.
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