General $N$-solitons and their dynamics in several nonlocal nonlinear Schrödinger equations
Author:
Preprint
Abstract
General $N$-solitons in three recently-proposed nonlocal nonlinear Schr\"odinger equations are presented. These nonlocal equations include the reverse-space, reverse-time, and reverse-space-time nonlinear Schr\"odinger equations, which are nonlocal reductions of the Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy. It is shown that general $N$-solitons in these different equations can be derived from the same Riemann-Hilbert solutions of the AKNS hierarchy, except that symmetry relations on the scattering data are different for these equations. This Riemann-Hilbert framework allows us to identify new types of solitons with novel eigenvalue configurations in the spectral plane. Dynamics of $N$-solitons in these equations is also explored. In all the three nonlocal equations, a generic feature of their solutions is repeated collapsing. In addition, multi-solitons can behave very differently from fundamental solitons and may not correspond to a nonlinear superposition of fundamental solitons.Keywords
All Related Versions
This publication has 23 references indexed in Scilit:
- Dynamics of rogue waves in the partially-symmetric nonlocal Davey–Stewartson systemsCommunications in Nonlinear Science and Numerical Simulation, 2019
- Soliton solutions of an integrable nonlocal modified Korteweg–de Vries equation through inverse scattering transformJournal of Mathematical Analysis and Applications, 2017
- Nonstandard bilinearization of-invariant nonlocal nonlinear Schrödinger equation: Bright soliton solutionsPhysics Letters A, 2017
- Nonlocal Fordy–Kulish equations on symmetric spacesPhysics Letters A, 2017
- On a nonlocal modified Korteweg-de Vries equation: Integrability, Darboux transformation and soliton solutionsCommunications in Nonlinear Science and Numerical Simulation, 2017
- Breathers and rogue waves for a third order nonlocal partial differential equation by a bilinear transformationApplied Mathematics Letters, 2016
- Integrable -symmetric local and nonlocal vector nonlinear Schrödinger equations: A unified two-parameter modelApplied Mathematics Letters, 2015
- Solitons, Nonlinear Evolution Equations and Inverse Scattering1991
- Integration of nonlinear equations of mathematical physics by the method of inverse scattering. IIFunctional Analysis and Its Applications, 1979
- The Inverse Scattering Transform‐Fourier Analysis for Nonlinear ProblemsStudies in Applied Mathematics, 1974