A note on Bäcklund transformations for the Harry Dym equation

Kai Tian; Mengyuan Cui; Q.P. Liu

Partial Differential Equations in Applied Mathematics (Jun 2022)

A note on Bäcklund transformations for the Harry Dym equation

Kai Tian,
Mengyuan Cui,
Q.P. Liu

Affiliations

Kai Tian: Department of Mathematics, China University of Mining and Technology, Beijing 100083, People’s Republic of China
Mengyuan Cui: Department of Mathematics, China University of Mining and Technology, Beijing 100083, People’s Republic of China
Q.P. Liu: Corresponding author.; Department of Mathematics, China University of Mining and Technology, Beijing 100083, People’s Republic of China

Journal volume & issue: Vol. 5
p. 100352

Abstract

Read online

The Bäcklund transformations are revisited for the Harry Dym equation. The associated nonlinear superposition formula, which consists of two equations — one for the field variable and the other for the spatial variable, is also presented. Interpreted as discrete systems, nonlinear superposition formula is identified as the lattice potential modified Korteweg–de Vries equation and a special case of Q1equation in the ABS list. A particular limit of the nonlinear superposition formula is considered and the resulting Bäcklund transformation is shown to be related to the finite transformation of the nonlocal symmetries.

Published in Partial Differential Equations in Applied Mathematics

ISSN: 2666-8181 (Online)
Publisher: Elsevier
Country of publisher: Netherlands
LCC subjects: Technology: Technology (General): Industrial engineering. Management engineering: Applied mathematics. Quantitative methods
Website: https://www.journals.elsevier.com/partial-differential-equations-in-applied-mathematics

About the journal

Abstract

Keywords