In this paper, the th Darboux transformations for the -dimensional generalized variable-coefficient Koretweg–de Vries (gvcKdV) equation are proposed. By using the Lamé function method, the generalized Lamé-type solutions for the linear spectral problem associated with the gvcKdV equation with the static and traveling Weierstrass elliptic -function potentials are derived, respectively. Then, the nonlinear wave solutions for the gvcKdV equation on the static and traveling Weierstrass elliptic -function periodic backgrounds under some constraint conditions are obtained, respectively, whose evolutions and dynamical properties are also discussed. The results show that the degenerate solutions on the periodic background can be obtained by taking the limits of the half-periods of , and the evolution curves of nonlinear wave solutions on the periodic background are determined by the coefficients of the gvcKdV equations.
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February 2024
Research Article|
February 28 2024
Breather wave solutions on the Weierstrass elliptic periodic background for the (2 + 1)-dimensional generalized variable-coefficient KdV equation Available to Purchase
Special Collection:
Rogue waves: Theory, Methods and Applications
Jiabin Li;
Jiabin Li
(Software, Validation, Writing – original draft)
1
School of Information Science, Zhejiang Ocean University
, Zhoushan 316022, China
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Yunqing Yang
;
Yunqing Yang
a)
(Funding acquisition, Supervision, Writing – review & editing)
2
School of Science, Zhejiang University of Science and Technology
, Hangzhou 310023, China
a)Author to whom correspondence should be addressed: [email protected]
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Wanyi Sun
Wanyi Sun
(Formal analysis, Methodology, Resources)
1
School of Information Science, Zhejiang Ocean University
, Zhoushan 316022, China
Search for other works by this author on:
1
School of Information Science, Zhejiang Ocean University
, Zhoushan 316022, China
2
School of Science, Zhejiang University of Science and Technology
, Hangzhou 310023, China
a)Author to whom correspondence should be addressed: [email protected]
Chaos 34, 023141 (2024)
Article history
Received:
December 18 2023
Accepted:
January 31 2024
Citation
Jiabin Li, Yunqing Yang, Wanyi Sun; Breather wave solutions on the Weierstrass elliptic periodic background for the (2 + 1)-dimensional generalized variable-coefficient KdV equation. Chaos 1 February 2024; 34 (2): 023141. https://doi.org/10.1063/5.0192185
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