Work

On the global existence for the modified Camassa–Holm equation

Year: 2025

Type: article

Abstract: The modified Camassa–Holm (mCH) equation is a model to describe the unidirectional propagation of shallow water waves. Without knowledge of any conservation quantities in the higher order Sobolev spaces for this type of the quasi‐linear evaluation equation, obtaining global well‐posedness for the mCH equation appears to be quite challenging. In this paper, we address the existence of global solutions in a weighted Sobolev space to the Cauchy problem for the mCH equation. The key to prove this result is establish bijectivity between potential and reflection coefficient by using inverse scattering transform method based on the Riemann–Hilbert problem associated with the Cauchy problem for the mCH equation.

Source: Journal of the London Mathematical Society

DOI: 10.1112/jlms.70232

Authors: Yiling Yang, Engui Fan, Yue Liu

Institutions: Chongqing University, Fudan University, The University of Texas at Arlington

Language: English

Topic: Nonlinear Waves and Solitons

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: bronze

Funder: National Natural Science Foundation of China

Awards: G3773207523, G7826363160