Riemann-Hilbert method and multi-soliton solutions for three-component coupled nonlinear Schrödinger equations. (English) Zbl 1427.35258
Summary: An integrable three-component coupled nonlinear Schrödinger (NLS) equation is considered in this work. We present the scattering and inverse scattering problems of the three-component coupled NLS equation by using the Riemann-Hilbert formulation. Furthermore, according to the Riemann-Hilbert method, the multi-soliton solutions of this equation are derived. We also analyze the collision dynamic behaviors of these solitons. Moreover, a new phenomenon for two-soliton collision is displayed, which is unique and not common in integrable systems. It is hoped that our results can help enrich the nonlinear dynamics of the NLS-type equations.
MSC:
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
| 35C08 | Soliton solutions |
| 37K15 | Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems |
| 35Q15 | Riemann-Hilbert problems in context of PDEs |
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
Keywords:
three-component coupled nonlinear Schrödinger equation; Riemann-Hilbert formulation; multi-soliton solutions; dynamic behaviorsReferences:
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