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

Chenglu Zhu; Lihua Wu; Chenglu Zhu; Lihua Wu

doi:10.3934/math.2025359

AIMS Mathematics

2025, Volume 10, Issue 4: 7828-7846. doi: 10.3934/math.2025359

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Research article

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

Received: 14 January 2025 Revised: 18 March 2025 Accepted: 26 March 2025 Published: 03 April 2025
MSC : 37K10, 35C08, 37K40

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.
- generalized WKI equation,
- Bäcklund transformation,
- soliton solutions
Citation: Chenglu Zhu, Lihua Wu. Bäcklund transformation and soliton solutions for a generalized Wadati-Konno-Ichikawa equation[J]. AIMS Mathematics, 2025, 10(4): 7828-7846. doi: 10.3934/math.2025359

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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.

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