Functional Solutions, Multi Line Solitons and Multiple Pole Solutions of the Generalized (2+1)-Dimensional Kaup-Kupershmidt Equation
Year: 2025
Author: Linlin Gui, Yufeng Zhang
Communications in Mathematical Research , Vol. 41 (2025), Iss. 2 : pp. 103–121
Abstract
The (2+1)-dimensional integrable generalization of the Kaup-Kupershmidt (KK) equation is solved by the inverse spectral transform method in this paper. Several new long derivative operators $V_x,$ $V_y$ and $V_t$ and the kernel functions $K$ of $\overline{∂}$-problem are introduced to construct a type of general solution of the KK equation. Based on these, several classes of the new exact solutions, with constant asymptotic values at infinity $u|_{x^2+y^2→∞} →0,$ for the KK equation are constructed via the $\overline{∂}$-dressing method.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cmr.2025-0008
Communications in Mathematical Research , Vol. 41 (2025), Iss. 2 : pp. 103–121
Published online: 2025-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: KK equation inverse scattering transform $\overline{∂}$-dressing method exact solution.