Work

The extended second Painlevé hierarchy: Auto-Bäcklund transformations and special integrals

Year: 2024

Type: article

Abstract: We return to our study of the extended second Painlevé hierarchy presented in a previous paper. For this hierarchy we give a new local auto-BT. We also give an extensive discussion of the iterative construction of solutions and special integrals using auto-BTs. Furthermore, we show that Lax pairs can be provided for special integrals. Even though this will, in fact, be the case quite generally, it seems that Lax pairs for special integrals have not been given previously. Amongst the equations for which we present Lax pairs are examples due to Cosgrove and, in classical Painlevé classification results, Chazy.

Source: Journal of Differential Equations

DOI: 10.1016/j.jde.2024.11.017

Authors: P.R. Gordoa, 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: $3,050

Funders: Universidad Rey Juan Carlos, Agencia Estatal de Investigación