Spectral problem for a two-component nonlinear Schrödinger equation in 2+1 dimensions: Singular manifold method and Lie point symmetries

P. Albares, J.M. Conde and P.G. Estévez

Applied Mathematics and Computation, 2019, vol. 355, issue C, 585-594

Abstract: An integrable two-component nonlinear Schrödinger equation in 2+1 dimensions is presented. The singular manifold method is applied in order to obtain a three-component Lax pair. The Lie point symmetries of this Lax pair are calculated in terms of nine arbitrary functions and one arbitrary constant that yield a non-trivial infinite-dimensional Lie algebra. The main non-trivial similarity reductions associated to these symmetries are identified. The spectral parameter of the reduced spectral problem appears as a consequence of one of the symmetries.

Keywords: Integrability; Lax pair; Lie symmetries; Nonlinear Schrödinger equation; Painleve property; Similarity reductions (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:355:y:2019:i:c:p:585-594

DOI: 10.1016/j.amc.2019.03.013

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