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Integrability, lump solutions, breather solutions and hybrid solutions for the (2+1)-dimensional variable coefficient Korteweg-de Vries equation

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Abstract

This paper focuses on the integrability and exact solutions of a (2+1)-dimensional variable coefficient Korteweg-de Vries equation. The bilinear form, Bäcklund transformations, and Lax pair of this equation are obtained using the Bell polynomial method. Soliton solutions, including lump solitons, breather solitons, and hybrid solutions, are constructed by assuming different auxiliary functions in the bilinear ansatz method. Additionally, the soliton solutions are presented as figures for different variable coefficient functions and undetermined items under appropriate parameter choices. The Bäcklund transformations also lead to Lax pair and the infinity conservation laws that ensure the integrability of the nonlinear system under study.

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Acknowledgements

This work is supported by the Beijing Natural Science Foundation (No. 1222005), Qin Xin Talents Cultivation Program of Beijing Information Science and Technology University (QXTCP C202118), the National Natural Science Foundation of China (No. 11905013).

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  1. School of Applied Science, Beijing Information Science and Technology University, Beijing, 100192, China

    Jingyi Chu, Xin Chen & Yaqing Liu

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  1. Jingyi Chu
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  2. Xin Chen
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  3. Yaqing Liu
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Contributions

Jingyi Chu: Writing-original draft, Data curation, Investigation. Xin Chen: Writing-review and editing. Yaqing Liu: Supervision, Validation.

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Correspondence to Yaqing Liu.

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Chu, J., Chen, X. & Liu, Y. Integrability, lump solutions, breather solutions and hybrid solutions for the (2+1)-dimensional variable coefficient Korteweg-de Vries equation. Nonlinear Dyn 112, 619–634 (2024). https://doi.org/10.1007/s11071-023-09062-w

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