Derivative non-linear Schr\"odinger equation: Singular manifold method and Lie symmetries
Abstract
We present a generalized study and characterization of the integrability properties of the derivative non-linear Schr\"odinger 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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