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On integrable wave interactions and Lax pairs on symmetric spaces

Gerdjikov, Vladimir S and Grahovski, Georgi G and Ivanov, Rossen I (2017) 'On integrable wave interactions and Lax pairs on symmetric spaces.' Wave Motion, 71. 53 - 70. ISSN 0165-2125

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Abstract

Multi-component generalizations of derivative nonlinear Schrödinger (DNLS) type of equations having quadratic bundle Lax pairs related to Z2-graded Lie algebras and A.III symmetric spaces are studied. The Jost solutions and the minimal set of scattering data for the case of local and nonlocal reductions are constructed. The latter lead to multi-component integrable equations with CPT-symmetry. Furthermore, the fundamental analytic solutions (FAS) are constructed and the spectral properties of the associated Lax operators are briefly discussed. The Riemann–Hilbert problem (RHP) for the multi-component generalizations of DNLS equation of Kaup–Newell (KN) and Gerdjikov–Ivanov (GI) types is derived. A modification of the dressing method is presented allowing the explicit derivation of the soliton solutions for the multi-component GI equation with both local and nonlocal reductions. It is shown that for specific choices of the reduction these solutions can have regular behavior for all finite x and t. The fundamental properties of the multi-component GI equations are briefly discussed at the end.

Item Type: Article
Uncontrolled Keywords: Lax representations, Symmetric spaces, Riemann–Hilbert problems, Dressing method, Soliton solutions, Local and nonlocal reductions
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science and Health > Mathematical Sciences, Department of
Depositing User: Jim Jamieson
Date Deposited: 05 Aug 2016 13:41
Last Modified: 21 Sep 2018 16:15
URI: http://repository.essex.ac.uk/id/eprint/17369

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