Derivative non-linear Schrödinger equation: Singular manifold method and Lie symmetries

Abstract

We present a generalized study and characterization of the integrability properties of the derivative non-linear Schrödinger equation in 1+1 dimensions. A Lax pair is derived for this equation by means of a Miura transformation and the singular manifold method. This procedure, together with the Darboux transformations, allow us to construct a wide class of rational soliton-like solutions. Lie classical symmetries have also been computed and similarity reductions have been analyzed and discussed.

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Cited by in corpus (3)

• Miura-reciprocal transformation and symmetries for the spectral problems of KdV and mKdV
• Integrability and rational soliton solutions for gauge invariant derivative nonlinear Schrödinger equations
• Spectral problem for the complex mKdV equation: singular manifold method and Lie symmetries