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2014•Symmetry Integrability and Geometry Methods and ApplicationsOpen access

Bäcklund-Darboux Transformations and Discretizations of Super KdV Equation

Lingling Xue

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Abstract

For a generalized super KdV equation, three Darboux transformations and the corresponding Bäcklund transformations are constructed.The compatibility of these Darboux transformations leads to three discrete systems and their Lax representations.The reduction of one of the Bäcklund-Darboux transformations and the corresponding discrete system are considered for Kupershmidt's super KdV equation.When all the odd variables vanish, a nonlinear superposition formula is obtained for Levi's Bäcklund transformation for the KdV equation.

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For a generalized super KdV equation, three Darboux transformations and the corresponding Bäcklund transformations are constructed.The compatibility of these Darboux transformations leads to three discrete systems and their Lax representations.The reduction of one of the Bäcklund-Darboux transformations and the corresponding discrete system are considered for Kupershmidt's super KdV equation.When all the odd variables vanish, a nonlinear superposition formula is obtained for Levi's Bäcklund transformation for the KdV equation.

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Available abstract

For a generalized super KdV equation, three Darboux transformations and the corresponding Bäcklund transformations are constructed.The compatibility of these Darboux transformations leads to three discrete systems and their Lax representations.The reduction of one of the Bäcklund-Darboux transformations and the corresponding discrete system are considered for Kupershmidt's super KdV equation.When all the odd variables vanish, a nonlinear superposition formula is obtained for Levi's Bäcklund transformation for the KdV equation.

Key concepts: Korteweg–de Vries equation, Mathematics, Darboux integral, Transformation (genetics), Nonlinear system, Compatibility (geochemistry), Superposition principle, Mathematical physics

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