Solitary Wave Solutions of Delayed Coupled Higgs Field Equation

• 作者: Shu Guan JI Xiao Wan LI
• 来源期刊: 数学学报（英文版）
• 年，卷（期）: 2022,（1）
• 页码范围: 97-106
• 页数: 10页
• 语种: 英文

摘要

This paper is devoted to the study of the solitary wave solutions for the delayed coupled Higgs field equation{utt-uxx-au+βf*u|u|2-2uv-τu(|u|2)x=0,vtt+vxx β(|u|2)xx=0.We first establish the existence of solitary wave solutions for the corresponding equation without delay and perturbation by using the Hamiltonian system method.Then we consider the persistence of solitary wave solutions of the delayed coupled Higgs field equation by using the method of dynamical system,especially the geometric singular perturbation theory,invariant manifold theory and Fredholm theory.According to the relationship between solitary wave and homoclinic orbit,the coupled Higgs field equation is transformed into the ordinary differential equations with fast variables by using the variable substitution.It is proved that the equations with perturbation also possess homoclinic orbit,and thus we obtain the existence of solitary wave solutions of the delayed coupled Higgs field equation.