基于双线性方法求两分量Coupled-Higgs方程的呼吸子解
Breather Solutions for the Two-Component Coupled-Higgs Equations Based on the Bilinear Method
摘要: 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。
Abstract: 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.
文章引用：吕梦琦. 基于双线性方法求两分量Coupled-Higgs方程的呼吸子解[J]. 理论数学, 2025, 15(5): 50-57. https://doi.org/10.12677/pm.2025.155152

参考文献

[1] Bludov, Y.V., Konotop, V.V. and Akhmediev, N. (2009) Matter Rogue Waves. Physical Review A, 80, Article 033610. [Google Scholar] [CrossRef] 
[2] Horikis, T.P. and Ablowitz, M.J. (2017) Rogue Waves in Nonlocal Media. Physical Review E, 95, Article 042211. [Google Scholar] [CrossRef] [PubMed]
[3] Ganshin, A.N., Efimov, V.B., Kolmakov, G.V., Mezhov-Deglin, L.P. and McClintock, P.V.E. (2008) Observation of an Inverse Energy Cascade in Developed Acoustic Turbulence in Superfluid Helium. Physical Review Letters, 101, Article 065303. [Google Scholar] [CrossRef] [PubMed]
[4] Bailung, H., Sharma, S.K. and Nakamura, Y. (2011) Observation of Peregrine Solitons in a Multicomponent Plasma with Negative Ions. Physical Review Letters, 107, Article 255005. [Google Scholar] [CrossRef] [PubMed]
[5] Solli, D.R., Ropers, C., Koonath, P. and Jalali, B. (2007) Optical Rogue Waves. Nature, 450, 1054-1057. [Google Scholar] [CrossRef] [PubMed]
[6] Zhang, H. and Chen, F. (2019) Dark and Antidark Solitons for the Defocusing Coupled Sasa-Satsuma System by the Darboux Transformation. Applied Mathematics Letters, 88, 237-242. [Google Scholar] [CrossRef] 
[7] Hirota, R. (2004) The Direct Method in Soliton Theory. Cambridge University Press.
[8] Hu, X., Li, C., Nimmo, J.J.C. and Yu, G. (2004) An Integrable Symmetric (2+1)-Dimensional Lotka-Volterra Equation and a Family of Its Solutions. Journal of Physics A: Mathematical and General, 38, 195-204. [Google Scholar] [CrossRef] 
[9] Weng, W. and Yan, Z. (2021) Inverse Scattering and N-Triple-Pole Soliton and Breather Solutions of the Focusing Nonlinear Schrödinger Hierarchy with Nonzero Boundary Conditions. Physics Letters A, 407, Article 127472. [Google Scholar] [CrossRef] 
[10] Anderson, D. (1998) Complex Variables, Introduction and Applications, by Mark J. Ablowitz and Athanassios S. Fokas. Optics & Photonics News, 9, 46-47.
[11] Tajiri, M. (1983) On N-Soliton Solutions of Coupled Higgs Field Equation. Journal of the Physical Society of Japan, 52, 2277-2280. [Google Scholar] [CrossRef] 
[12] Tsegel’nik, V.V. (2000) Self-similar Solutions of a System of Two Nonlinear Partial Differential Equations. Differential Equations, 36, 480-482. [Google Scholar] [CrossRef] 
[13] Tang, W. (2023) Soliton Dynamics to the Higgs Equation and Its Multi-Component Generalization. Wave Motion, 120, Article 103144. [Google Scholar] [CrossRef] 
[14] Ling, L., Zhao, L.-C. and Guo, B. (2014) Darboux Transformation and Classification of Solution for Mixed Coupled Nonlinear Schrödinger Equations. Communications in Nonlinear Science & Numerical Simulation, 32, 285-304. [Google Scholar] [CrossRef] 
[15] Zha, Q.L. (2020) Dynamics of Localized Wave Solutions for the Coupled Higgs Field Equation. Nonlinear Dynamics, 101, 1181-1198. [Google Scholar] [CrossRef] 
[16] Hirota, R. (1971) Exact Solution of the Korteweg—De Vries Equation for Multiple Collisions of Solitons. Physical Review Letters, 27, 1192-1194. [Google Scholar] [CrossRef] 
[17] 陈登远. 孤子引论[M]. 上海: 科学出版社, 2006.

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