$\varphi^4$ 模型中 kink-antikink 构型下 sine-Gordon 双孤子解的形变
Deformation of sine-Gordon two-soliton solutions in $φ^4$ kink-antikink configurations
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中文总结 AI 辅助
本文通过场形变将 sine-Gordon 双孤子解映射到 $\varphi^4$ 模型，构造 kink-antikink 构型，发现小间距下映射构型残差小于叠加 Ansatz，为散射数值研究提供初始数据。
中文摘要 AI 辅助
在这项工作中，我们通过场形变将可积 sine-Gordon 系统的精确解映射到不可积的 $\varphi^4$ 模型中，从而构造解析的 kink-antikink ($K\bar{K}$) 构型。这一过程产生了两类不同的构型，由初始半间距和速度参数化。我们将这些轮廓与标准的加性叠加 Ansatz 在真空结构和运动方程残差方面进行比较，推导出相应的积分平方残差的显式闭式表达式。对于小间距，映射的孤子-反孤子构型比朴素叠加 Ansatz 表现出明显更小的残差，而后者又比映射的双孤子构型表现更好。尽管映射场不是 $\varphi^4$ 运动方程的精确解，但它们为 kink-antikink 散射和共振现象的数值研究提供了数学上一致、拓扑上合理且物理上动机明确的初始数据。
英文摘要
In this work, we construct analytical kink-antikink $(K\bar{K})$ configurations in the non-integrable $φ^4$ model by mapping exact solutions of the integrable sine-Gordon system via a field deformation. This procedure yields two distinct classes of configurations, parametrized by the initial half-separation and velocity. We compare these profiles with the standard additive superposition Ansatz in terms of vacuum structure and equation-of-motion residuals, deriving explicit closed-form expressions for the corresponding integrated squared residuals. For small separations, the mapped soliton-antisoliton configurations exhibit appreciably smaller residuals than the naive superposition Ansatz, which in turn performs better than the mapped two-soliton configurations. Although the mapped fields are not exact solutions of the $φ^4$ equation of motion, they provide mathematically consistent, topologically sound, and physically motivated initial data for numerical studies of kink-antikink scattering and resonance phenomena.
发表机构
- Alikhanyan National Laboratory (Yerevan Physics Institute)（阿利哈尼扬国家实验室（叶里万物理研究所））
- Department of Physics, Qu.C., Islamic Azad University（伊斯兰阿扎德大学奎钦分校物理系）
- Coordenação do Curso de Física - Bacharelado & Programa de Pós-Graduação em Física, Universidade Federal do Maranhão (UFMA)（马拉尼昂联邦大学物理本科课程协调处及物理研究生项目）
- Institute of Modern Physics（现代物理研究所）
- University of the Chinese Academy of Sciences（中国科学院大学）
- Department of Physics, Federal University of Paraíba（帕拉伊巴联邦大学物理系）
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