Work

A new approach to deriving Bäcklund transformations

Year: 2024

Type: article

Abstract: We give a new, surprisingly simple approach to the derivation of Bäcklund transformations. Motivated by the use of integrating factors to solve linear ordinary differential equations , for the nonlinear case this new technique leads to differential relations between equations. Although our interest here is in Painlevé equations, our approach is applicable to nonlinear equations more widely. As a completely new result we obtain a matrix version of a classical mapping between solutions of special cases of the second Painlevé equation. This involves the derivation of a new matrix second Painlevé equation, for which we also present a Lax pair. In addition, we give a matrix version of the Schwarzian second Painlevé equation, again a completely new result. In this way we also discover a new definition of matrix Schwarzian derivative.

Source: Journal of Mathematical Analysis and Applications

DOI: 10.1016/j.jmaa.2024.129052

Author: A. Pickering

Institution: Universidad Rey Juan Carlos

Language: English

Topic: Nonlinear Waves and Solitons

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,100

Funders: Ministerio de Ciencia e Innovación, Universidad Rey Juan Carlos, Agencia Estatal de Investigación