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Pure Mathematics 2025
基于双线性方法求两分量Coupled-Higgs方程的呼吸子解
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Abstract:
呼吸子解作为一种重要的局域波解，在非线性波动力学中扮演重要的角色。本文利用Hirota双线性方法，构造出Coupled-Higgs方程的双线性形式，然后结合特殊的幂级数展开，求出Coupled-Higgs方程的呼吸II型解，为了进一步验证和展示理论结果，利用Mathematica对呼吸波进行了可视化。
Breather solutions, as an important type of localized wave solution, play a significant role in nonlinear wave dynamics. In this paper, the Hirota bilinear method is employed to construct the bilinear form of the Coupled-Higgs equation. Then, by combining a special power series expansion, the Breather Type II solutions of the Coupled-Higgs equation are derived. To further validate and illustrate the theoretical results, the breather waves are visualized using Mathematica.
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