具有步进初始数据的非局部kundu -非线性Schrödinger方程的多孤子解

IF 1.4 4区物理与天体物理 Q2 MATHEMATICS, APPLIED

Journal of Nonlinear Mathematical Physics Pub Date : 2023-10-30 DOI:10.1007/s44198-023-00149-x

Ling Lei, Shou-Fu Tian, Yan-Qiang Wu

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引用次数: 0

摘要

研究了具有步长初始数据的非局部kundu -非线性Schrödinger (NK-NLS)方程Cauchy问题的多孤子解。首先对NK-NLS方程的Lax对进行了谱分析，然后基于Jost解和谱函数的解析性、对称性和渐近性，建立了方程的Riemann-Hilbert (RH)问题。由于阶跃初值的影响，需要考虑RH问题在原点处的奇异性条件，该奇异性条件可以转化为残差条件。进一步，根据相应的RH问题，得到了NK-NLS方程的多孤子解。

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Multi-Soliton Solutions for the Nonlocal Kundu-Nonlinear Schrödinger Equation with Step-Like Initial Data

Abstract We investigate the multi-soliton solutions for the Cauchy problem of the nonlocal Kundu-nonlinear Schrödinger (NK-NLS) equation with step-like initial data. We first perform the spectral analysis on the Lax pair of the NK-NLS equation, and then establish the Riemann-Hilbert (RH) problem of the equation based on the analytic, symmetric and asymptotic properties of Jost solutions and spectral functions. Because of the influence of step-like initial value, we need to consider the singularity condition of the RH problem at the origin, and this singularity condition can be converted to a residue condition. Further, the multi-soliton solutions of the NK-NLS equation are obtained in terms of the corresponding RH problem.

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来源期刊

Journal of Nonlinear Mathematical Physics PHYSICS, MATHEMATICAL-PHYSICS, MATHEMATICAL

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

3 months

期刊介绍： Journal of Nonlinear Mathematical Physics (JNMP) publishes research papers on fundamental mathematical and computational methods in mathematical physics in the form of Letters, Articles, and Review Articles. Journal of Nonlinear Mathematical Physics is a mathematical journal devoted to the publication of research papers concerned with the description, solution, and applications of nonlinear problems in physics and mathematics. The main subjects are: -Nonlinear Equations of Mathematical Physics- Quantum Algebras and Integrability- Discrete Integrable Systems and Discrete Geometry- Applications of Lie Group Theory and Lie Algebras- Non-Commutative Geometry- Super Geometry and Super Integrable System- Integrability and Nonintegrability, Painleve Analysis- Inverse Scattering Method- Geometry of Soliton Equations and Applications of Twistor Theory- Classical and Quantum Many Body Problems- Deformation and Geometric Quantization- Instanton, Monopoles and Gauge Theory- Differential Geometry and Mathematical Physics