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Research Article | Open Access

Bäcklund transformation and soliton solutions for a generalized Wadati-Konno-Ichikawa equation

Chenglu Zhu, Lihua Wu( )
School of Mathematical Sciences, Huaqiao University, Quanzhou, Fujian 362021, China
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Abstract

By employing a reciprocal transformation, we relate the generalized Wadati–Konno–Ichikawa (gWKI) equation to an associated gWKI (agWKI) equation. Utilizing the Darboux transformation of the agWKI equation and Bianchi's theorem of permutability, we derive the N-Bäcklund transformation for the gWKI equation. As an application, we obtain some soliton solutions for the gWKI equation, including smooth solitons, bursting solitons, and loop-type solitons. Furthermore, we explore the interactions between two solitons.

Keywords

generalized WKI equationBäcklund transformationsoliton solutions
CLC number: 37K10, 35C08, 37K40

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AIMS Mathematics
Volume 10 Issue 4,
April 2025
Pages 7828-7846
DOI: 10.3934/math.2025359

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Cite this article:
Zhu C, Wu L. Bäcklund transformation and soliton solutions for a generalized Wadati-Konno-Ichikawa equation. AIMS Mathematics, 2025, 10(4): 7828-7846. https://doi.org/10.3934/math.2025359

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Received: 14 January 2025
Revised: 18 March 2025
Accepted: 26 March 2025
Published: 15 April 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)