A new integrable generalization of the Korteweg - de Vries equation
Ayse Karasu-Kalkanli, Atalay Karasu, Anton Sakovich, Sergei Sakovich,, Refik Turhan
TL;DR
This paper introduces a new sixth-order integrable nonlinear wave equation related to the Korteweg-de Vries equation, providing its Lax pair, Bäcklund transformation, and solutions, expanding the understanding of integrable systems.
Contribution
It presents a novel integrable sixth-order nonlinear wave equation, along with its Lax representation, Bäcklund transformation, and explicit solutions, which was not previously known.
Findings
Discovered a new integrable sixth-order wave equation.
Derived its Lax pair and Bäcklund transformation.
Analyzed its traveling wave solutions and symmetries.
Abstract
A new integrable sixth-order nonlinear wave equation is discovered by means of the Painleve analysis, which is equivalent to the Korteweg - de Vries equation with a source. A Lax representation and a Backlund self-transformation are found of the new equation, and its travelling wave solutions and generalized symmetries are studied.
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