A new integrable generalization of the Korteweg - de Vries equation

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.

💡 Research Summary

The paper introduces a previously unknown sixth‑order nonlinear wave equation that is integrable in the sense of the Painlevé property. By performing a systematic Painlevé analysis, the authors identify a specific set of relations among the coefficients of the generic sixth‑order equation

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