This article is cited in 2 papers

Nonlocality, integrability, and solitons

Wen-Xiu Ma<sup>abcde

a</sup> Department of Mathematics, Zhejiang Normal University, Zhejiang, China
^b Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia
^c Department of Mathematics and Statistics, University of South Florida, Tampa, USA
^d School of Mathematics, South China University of Technology, Guangzhou, Guangzhou, China
^e Material Science Innovation and Mode, Mafikeng Campus, Mmabatho, South Africalling, Department of Mathematical Sciences, North-West University

Abstract: We explore integrable equations that involve involution points, along with the solution phenomena for Cauchy problems associated with nonlocal differential equations. By applying group reductions to classical Lax pairs, we generate nonlocal integrable equations. Soliton solutions of these models are derived using binary Darboux transformations or reflectionless Riemann–Hilbert problems in the nonlocal context. Further discussion on the well-posedness of nonlocal differential equations is also presented.

Keywords: Lax pair, integrable model, Darboux transformation.

Received: 30.01.2025
Revised: 03.03.2025

DOI: 10.4213/tmf10916

 English version: Theoretical and Mathematical Physics, 2025, 224:1, 1220–1233

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