Miura and Generalized B\"acklund Transformation for KdV Hierarchy
J. F. Gomes, A. L. Retore, A. H. Zimerman
TL;DR
This paper explores the derivation of B"acklund transformations for the KdV hierarchy using gauge transformations related to the Miura transformation, linking KdV and mKdV equations.
Contribution
It presents a novel derivation of B"acklund transformations for the KdV hierarchy via gauge transformations derived from the Miura transformation.
Findings
Derived B"acklund transformation for KdV hierarchy
Connected KdV and mKdV equations through gauge transformations
Provided a new perspective on integrable hierarchy transformations
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 B\"acklund transformation and its Miura-gauge transformation connecting both hierarchies.
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