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Riemann–Hilbert method and multi-soliton solutions of the Kundu-nonlinear Schrödinger equation
Authors:Yan  Xue-Wei
Institution:1.School of Mathematical Sciences, Huaibei Normal University, Huaibei, 235000, People’s Republic of China
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Abstract:

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.

Keywords:
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