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Explicit Traveling Wave Solutions and Their Dynamical Behaviors for the Coupled Higgs Field Equation
  
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KeyWord:Coupled Higgs field equation; Traveling wave solutions; Kink wave solutions
Author NameAffiliation
Keqin Zhao School of Mathematical Sciences, Huaqiao University, Quanzhou, Fujian 362021, China 
Zhenshu Wen School of Mathematical Sciences, Huaqiao University, Quanzhou, Fujian 362021, China 
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Abstract:
      In this paper, we focus on the traveling wave solutions of the coupled Higgs field equation from the perspective of dynamical systems. Through the phase portraits, in addition to periodic wave solutions and solitary wave solutions, we also obtain explicit periodic singular wave solutions, singular wave solutions and kink wave solutions, which were not found in the previous works. The dynamical behavior of these solutions and their internal relations are revealed through asymptotic analysis. The results will help supplement the study of field equation.