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Symmetry
Volume 18
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10.3390/sym18020242
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Article

Nonlinear Dynamics of M-Lump and Hybrid Solutions of a Novel (2+1)-Dimensional Generalized Sawada-Kotera Equation

by
Xuan Wang
1,
Jian-Ping Yu
2 and
Yong-Li Sun
1,*
1
Department of Mathematics, School of Mathematics and Physics, Beijing University of Chemical Technology, Beijing 100029, China
2
Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 2Y2, Canada
*
Author to whom correspondence should be addressed.
Symmetry 2026, 18(2), 242; https://doi.org/10.3390/sym18020242
Submission received: 26 August 2025 / Revised: 21 January 2026 / Accepted: 28 January 2026 / Published: 29 January 2026
(This article belongs to the Special Issue Symmetry in Integrable Systems: Topics and Advances)
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Abstract

In this study, a novel (2+1)-dimensional generalized Sawada-Kotera (gSK) equation is first proposed, followed by the derivation of its corresponding Hirota bilinear form (bgSK). Utilizing the Hirota direct method and the “long-wave” limit of its N-soliton solutions, we obtain M-lump solutions that decay to a uniform background state in all spatial directions. Furthermore, we construct hybrid solutions consisting of M-lump and line-soliton (stripe-soliton) interactions. Finally, the dynamic properties and evolutionary behavior of these solutions are illustrated through detailed numerical simulations and graphical analysis.
Keywords: M-lump solutions; hybrid solutions; hirota bilinear operators; (2+1)-dimensional generalized Sawada-Kotera equation; soliton interactions M-lump solutions; hybrid solutions; hirota bilinear operators; (2+1)-dimensional generalized Sawada-Kotera equation; soliton interactions

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MDPI and ACS Style

Wang, X.; Yu, J.-P.; Sun, Y.-L. Nonlinear Dynamics of M-Lump and Hybrid Solutions of a Novel (2+1)-Dimensional Generalized Sawada-Kotera Equation. Symmetry 2026, 18, 242. https://doi.org/10.3390/sym18020242

AMA Style

Wang X, Yu J-P, Sun Y-L. Nonlinear Dynamics of M-Lump and Hybrid Solutions of a Novel (2+1)-Dimensional Generalized Sawada-Kotera Equation. Symmetry. 2026; 18(2):242. https://doi.org/10.3390/sym18020242

Chicago/Turabian Style

Wang, Xuan, Jian-Ping Yu, and Yong-Li Sun. 2026. "Nonlinear Dynamics of M-Lump and Hybrid Solutions of a Novel (2+1)-Dimensional Generalized Sawada-Kotera Equation" Symmetry 18, no. 2: 242. https://doi.org/10.3390/sym18020242

APA Style

Wang, X., Yu, J.-P., & Sun, Y.-L. (2026). Nonlinear Dynamics of M-Lump and Hybrid Solutions of a Novel (2+1)-Dimensional Generalized Sawada-Kotera Equation. Symmetry, 18(2), 242. https://doi.org/10.3390/sym18020242

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