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Auto-Bäcklund Transformation and Exact Solutions for a New Integrable (3+1)-dimensional KdV-CBS Equation

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Abstract

The Korteweg-de Vries–Calogero–Bogoyavlenskii–Schiff (KdV-CBS) equation is often used in dealing with long-wave propagation interactions, and is widely used in mathematics, physics, and engineering. This paper proposes a new extended (3+1)-dimensional KdV-CBS equation, and it’s never been studied. Additionally, we verify the integrability of the equation based on the Painlevé test. By employing Hirota’s method, a bilinear auto-Bäcklund transformation, the multiple-soliton solutions, and the soliton molecules of the equation are derived. New exact solutions of the equation are constructed utilizing the power series expansion method and \((G'/G)\)-expansion method. These exact solutions are also presented graphically. Finally, the conservation laws of the equation are obtained. Our results are helpful for understanding nonlinear wave phenomena.

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All authors contributed to the study conception and design. The first draft of the manuscript was written by Xinyue Guo and Lianzhong Li. All authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Guo, X., Li, L. Auto-Bäcklund Transformation and Exact Solutions for a New Integrable (3+1)-dimensional KdV-CBS Equation. Qual. Theory Dyn. Syst. 23, 207 (2024). https://doi.org/10.1007/s12346-024-01062-4

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