Several novel rational solutions with nonzero boundary condition for the Kundu equation, which is an important physical model, are derived using the technique of generalized Darboux transformation. It is the first time that a systemic analysis has been conducted on such rational solutions for the Kundu equation. For the 1-order rational solutions with nonzero boundary conditions, our findings reveal that three parameters, a, b, and β, which are associated with the effects of self-steepening, self-phase modulation, and quintic nonlinearity in the Kundu equation, can result in four distinct states for case B and five distinct states for case C, all corresponding to rational solutions with nonzero boundary conditions.

中文翻译：

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具有非零边界条件的 Kundu 方程的有理解的状态转换


Kundu 方程是一个重要的物理模型，其边界条件为非零，使用广义 Darboux 变换技术推导了几种新颖的有理解。这是第一次对 Kundu 方程的这种有理解进行系统分析。对于具有非零边界条件的一阶有理解，我们的研究结果表明，与昆杜方程中自陡化、自相位调制和五次非线性的影响相关的三个参数 a、b 和 β 可以导致情况 B 的四种不同状态和情况 C 的五种不同状态，所有这些都对应于具有非零边界条件的有理解。