Bifurcations of Exact Travelling Wave Solutions to Coupled Higgs Equations and Maccari Systems
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摘要: 利用动力系统方法，对耦合Higgs方程和Maccari系统的定性行为和行波解进行了研究.基于这种方法，给出了系统在不同参数条件下的相图，得到了包括孤立波解和周期波解在内的行波解.运用数值模拟的方法，对方程的光滑孤立波解和周期波解进行了数值模拟.获得的结果完善了相关文献已有的研究成果.Abstract: With the dynamical system method, the qualitative performance of and the exact travelling wave solutions to the coupled Higgs equations and the Maccari systems were studied. Based on this method, all phase portraits of the systems in the parametric space were given. All possible bounded travelling wave solutions such as the solitary wave solutions and the periodic travelling wave solutions were obtained. Through numerical simulation, the smooth solitary wave solutions and the periodic travelling wave solutions were picturized. The results show that the present findings improve the related previous conclusions.
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Key words:
- coupled Higgs equation /
- Maccari system /
- dynamical system /
- travelling wave solution /
- bifurcation
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