In this work, we study the Kundu-nonlinear Schrödinger (Kundu-NLS) equation (so-called the extended NLS equation), which can describe the propagation of the waves in dispersive media. A Lax spectral problem is used to construct the Riemann–Hilbert problem, via a matrix transformation. Based on the inverse scattering transformation, the general solutions of the Kundu-NLS equation are calculated. In the reflection-less case, the special matrix Riemann–Hilbert problem is carefully proposed to derive the multi-soliton solutions. Finally, some novel dynamics behaviors of the nonlinear system are theoretically and graphically discussed.

中文翻译：

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Riemann–Hilbert方法和Kundu-非线性Schrödinger方程的多孤子解

在这项工作中，我们研究了Kundu非线性Schrödinger（Kundu-NLS）方程（所谓的扩展NLS方程），该方程可以描述波在分散介质中的传播。Lax谱问题用于通过矩阵变换来构造Riemann-Hilbert问题。基于逆散射变换，计算了Kundu-NLS方程的一般解。在无反射的情况下，仔细地提出了特殊的矩阵黎曼-希尔伯特问题来推导多孤子解。最后，从理论上和图形上讨论了非线性系统的一些新颖的动力学行为。