发表机构
Gebze Technical University; Bogazici University; Khazar University（盖布泽理工大学; 博阿齐奇大学; 哈扎尔大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文运用逆散射方法推导了耦合负一阶克莱因-戈登方程的N孤子解，构造了其守恒律等结构，建立了核函数与势的对应关系，为该类耦合非线性方程的求解提供了新途径。
AI 中文摘要
通过Gelfand-Levitan-Marchenko方程，运用逆散射方法，针对满足消失边界条件的耦合负一阶克莱因-戈登（CNKG）方程，推导得到了精确的N孤子解。基于零曲率表示，构造了前述耦合非线性方程的守恒律、运动积分以及哈密顿结构。回顾了Manakov谱问题中的Jost函数及其解析性质。随后利用本征函数的积分方程构建了Gel'fand-Levitan-Marchenko方程。求解这些方程建立了核函数与势之间的直接对应关系，得到了一般形式的N孤子表达式。
英文摘要
The exact N-soliton solutions are derived for the coupled negative first order Klein-Gordon (CNKG) equation subject to vanishing boundary conditions by using the inverse scattering method via Gelfand-Levitan-Marchenko equation. Based on the zero-curvature representation, the conservation laws, integrals of motion, and Hamiltonian structure of the aforementioned coupled nonlinear equations are constructed. The Jost functions and their analyticity properties for the Manakov spectral problem are recalled. The integral equations for the eigenfunctions are then used to formulate the Gel'fand-Levitan-Marchenko equations. Solving these equations establishes a direct correspondence between the kernel functions and the potential, yielding the general N-soliton expressions.
Comments21 pages
