期刊
THEORETICAL AND MATHEMATICAL PHYSICS
卷 197, 期 1, 页码 1430-1450出版社
MAIK NAUKA/INTERPERIODICA/SPRINGER
DOI: 10.1134/S0040577918100033
关键词
integrable system; multicomponent nonlinear Schrodinger equation; Lax representation; Zakharov-Shabat system; spectral decompositions; PT symmetry; inverse scattering transform; Riemann-Hilbert problem; dressing method
Our aim is to develop the inverse scattering transform for multicomponent generalizations of nonlocal reductions of the nonlinear Schrodinger (NLS) equation with symmetry related to symmetric spaces. This includes the spectral properties of the associated Lax operator, the Jost function, the scattering matrix, the minimum set of scattering data, and the fundamental analytic solutions. As main examples, we use theManakov vector Schrodinger equation (related to A.III-symmetric spaces) and the multicomponent NLS (MNLS) equations of Kulish-Sklyanin type (related to BD.I-symmetric spaces). Furthermore, we obtain one- and two-soliton solutions using an appropriate modification of the Zakharov-Shabat dressing method. We show that the MNLS equations of these types admit both regular and singular soliton configurations. Finally, we present different examples of one- and two-soliton solutions for both types of models, subject to different reductions.
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