Work

On a Generalized Camassa–Holm Equation Describing Pseudospherical Surfaces

Year: 2025

Type: article

Abstract: In this paper, a new integrable Camass–Holm type equation with cubic nonlinearity is studied. The Lie symmetries and group-invariant solutions of the equation are presented. Geometrically, this equation describes a non-trivial one-parameter family of pseudo-spherical surfaces and is the integrability condition of an $\mathfrak {sl}(2, \mathbb {R})$ -valued linear problem. Moreover, its quadratic pseudo-potentials and infinite number of conservation laws are directly constructed. In addition, the equation is proved to possesses the property of admitting local isometric immersions in $\mathbb {E}^3$ with the “universal" coefficients of the second fundamental form, which depend only on x and t .

Source: Journal of Nonlinear Mathematical Physics

DOI: 10.1007/s44198-025-00365-7

Authors: Mingyue Guo, Zhenhua Shi

Institution: Northwest University

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: $1,490

Funder: Northwest University