Nonlocal Yajima-Oikawa system: binary Darboux transformation, exact solutions and dynamic properties. (English) Zbl 1534.35376
Summary: The Yajima-Oikawa (YO) system is an important long-wave-short-wave resonant interaction model, which can be used to describe a fascinating resonance phenomena in diverse areas, such as hydrodynamics, nonlinear optics and biophysics. In this paper, we propose a new type integrable nonlocal YO system, which can be derived from the special reduction in the two-component YO system. We show that the binary Darboux transformation is an effective method to construct not only multi-soliton solutions, but also other types of solutions for this type nonlocal integrable systems. Additionally, some novel solutions of the nonlocal YO system are obtained, and further are analyzed in detail to reveal several interesting dynamic features, such as the moving bright soliton with sudden position shift, the collision of two-breather waves.
MSC:
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
| 35Q41 | Time-dependent Schrödinger equations and Dirac equations |
| 35Q51 | Soliton equations |
| 35C08 | Soliton solutions |
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
| 37K15 | Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems |
| 37K35 | Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems |
| 35B34 | Resonance in context of PDEs |
| 35C05 | Solutions to PDEs in closed form |
Keywords:
nonlocal nonlinear Schrödinger equation; nonlocal Yajima-Oikawa system; binary Darboux transformation; exact solutionsReferences:
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