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

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.

References in corpus (4)

• Symmetry Reductions of the Lax Pair of the Four-Dimensional Euclidean Self-Dual Yang-Mills Equations
• Spin dynamics in helical molecules with non-linear interactions
• Chiral solitons in a non-linear model of helical molecules
• Classical Lie symmetries and reductions for a generalized NLS equation in 2+1 dimensions

Cited by in corpus (2)

• Miura-reciprocal transformation and symmetries for the spectral problems of KdV and mKdV
• Spectral problem for the complex mKdV equation: singular manifold method and Lie symmetries