On nonlocal reductions of the multi-component nonlinear Schrodinger equation on symmetric spaces
arXiv:1711.10833 · doi:10.1134/S0040577918100033
Abstract
The aim of this paper is to develop the inverse scattering transform (IST) for multi-component generalisations of nonlocal reductions of the nonlinear Schrodinger (NLS) equation with PT-symmetry related to symmetric spaces. This includes: the spectral properties of the associated Lax operator, Jost function, the scattering matrix and the minimal set of scattering data, the fundamental analytic solutions. As main examples, we use the Manakov vector Schrödinger equation (related to A.III-symmetric spaces) and the multi-component NLS (MNLS) equations of Kullish-Sklyanin type (related to BD.I-symmetric spaces). Furthermore, the 1- and 2-soliton solutions are obtained by using an appropriate modification of the Zakharov-Shabat dressing method. It is shown, that the MNLS equations of these types allow both regular and singular soliton configurations. Finally, we present here different examples of 1- and 2-soliton solutions for both types of models, subject to different reductions.
20 pages, LaTeX, no figures
References in corpus (11)
- Making Sense of Non-Hermitian Hamiltonians
- Solitons in PT-symmetric nonlinear lattices
- PT-symmetric Deformations of the Korteweg-de Vries Equation
- Hamiltonian formulation of the standard -symmetric nonlinear Schrödinger dimer
- Nonlocal Fordy - Kulish Equations on Symmetric Spaces
- PT-symmetric deformations of integrable models
- On integrable wave interactions and Lax pairs on symmetric spaces
- Multi-Component NLS Models on Symmetric Spaces: Spectral Properties versus Representations Theory
- On nonlocal models of Kulish-Sklyanin type and generalized Fourier transforms
- Kulish-Sklyanin type models: integrability and reductions
- On the Caudrey-Beals-Coifman System and the Gauge Group Action