Miura and Generalized Bäcklund Transformation for KdV Hierarchy

Abstract

Using the fact that Miura transformation can be expressed in the form of gauge transformation connecting the KdV and mKdV equations, we discuss the derivation of the Bäcklund transformation and its Miura-gauge transformation connecting both hierarchies.

arXiv comment21 pages

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Cited by in corpus (11)

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• Common Hirota Form Bäcklund Transformation for the Unified Soliton System
• Gauge Symmetry Origin of Bäcklund Transformations for Painlevé Equations
• Comments on the negative grade KdV hierarchy
• SKdV, SmKdV flows and their supersymmetric gauge-Miura transformations
• Twisted Affine Integrable Hierarchies and Soliton Solutions
• Quantum Integrability and Quantum Groups: a special issue in memory of Petr P. Kulish
• An integrable hierarchy associated with loop extension of ${\mathbb{Z}}_2^2$-graded $\mathfrak{osp}(1|2)$
• New negative grade solitonic sector for supersymmetric KdV and mKdV hierarchies