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Several types of periodic wave solutions and their relations of a Fujimoto--Watanabe equation
Lijuan Shi,Zhenshu Wen
Keywords:Fujimoto--Watanabe equation; Dynamics; Periodic wave solutions; Solitary wave solutions; Relations
      In this paper, we study periodic wave solutions of a Fujimoto--Watanabe equation by exploiting the bifurcation method of dynamical systems. We obtain all possible bifurcations of phase portraits of the system in different regions of the parametric space, and then give the sufficient conditions to guarantee the existence of several types of periodic wave solutions. What"s more, we present their exact expressions and reveal their inside relations as well as their relations with solitary wave solutions.