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- Title
Multi-Soliton Solutions for the Nonlocal Kundu-Nonlinear Schrödinger Equation with Step-Like Initial Data.
- Authors
Lei, Ling; Tian, Shou-Fu; Wu, Yan-Qiang
- 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.
- Subjects
SCHRODINGER equation; CAUCHY problem; RIEMANN-Hilbert problems; LAX pair
- Publication
Journal of Nonlinear Mathematical Physics, 2023, Vol 30, Issue 4, p1661
- ISSN
1402-9251
- Publication type
Article
- DOI
10.1007/s44198-023-00149-x