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arXiv · 2010.09411

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

Paz Albares·Pilar García Estévez·Juan Domingo Lejarreta
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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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Paz Albares, Pilar García Estévez, Juan Domingo Lejarreta. 2020-10-19. Derivative non-linear Schrödinger equation: Singular manifold method and Lie symmetries. https://doi.org/10.1016/j.amc.2021.126089

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