A Two-Component Generalization of the Integrable rdDym Equation
Oleg I. Morozov
TL;DR
This paper introduces a new two-component generalization of the integrable rdDym equation, connecting it with known equations and establishing a Bäcklund transformation to Bogdanov's hierarchy, expanding the understanding of integrable systems.
Contribution
It presents a novel two-component integrable generalization of the rdDym equation and links it to existing equations via a Bäcklund transformation.
Findings
Includes reductions to rdDym, Boyer-Finley, and deformed Boyer-Finley equations.
Establishes a Bäcklund transformation with Bogdanov's hierarchy.
Expands the class of known integrable two-component equations.
Abstract
We find a two-component generalization of the integrable case of rdDym equation. The reductions of this system include the general rdDym equation, the Boyer-Finley equation, and the deformed Boyer-Finley equation. Also we find a B\"acklund transformation between our generalization and Bodganov's two-component generalization of the universal hierarchy equation.
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