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Volume 41, Issue 2
Functional Solutions, Multi Line Solitons and Multiple Pole Solutions of the Generalized (2+1)-Dimensional Kaup-Kupershmidt Equation

Linlin Gui & Yufeng Zhang

DOI: 10.4208/cmr.2025-0008

Commun. Math. Res., 41 (2025), pp. 103-121.

Published online: 2025-06

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  • 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.

  • Keywords

KK equation, inverse scattering transform, $\overline{∂}$-dressing method, exact solution.

  • AMS Subject Headings

35C08, 45G15, 45Q05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-41-103, author = {Gui , Linlin and Zhang , Yufeng}, title = {Functional Solutions, Multi Line Solitons and Multiple Pole Solutions of the Generalized (2+1)-Dimensional Kaup-Kupershmidt Equation}, journal = {Communications in Mathematical Research }, year = {2025}, volume = {41}, number = {2}, pages = {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.

}, issn = {2707-8523}, doi = {https://doi.org/10.4208/cmr.2025-0008}, url = {http://global-sci.org/intro/article_detail/cmr/24187.html} }
TY - JOUR T1 - Functional Solutions, Multi Line Solitons and Multiple Pole Solutions of the Generalized (2+1)-Dimensional Kaup-Kupershmidt Equation AU - Gui , Linlin AU - Zhang , Yufeng JO - Communications in Mathematical Research VL - 2 SP - 103 EP - 121 PY - 2025 DA - 2025/06 SN - 41 DO - http://doi.org/10.4208/cmr.2025-0008 UR - https://global-sci.org/intro/article_detail/cmr/24187.html KW - KK equation, inverse scattering transform, $\overline{∂}$-dressing method, exact solution. AB -

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.

Gui , Linlin and Zhang , Yufeng. (2025). Functional Solutions, Multi Line Solitons and Multiple Pole Solutions of the Generalized (2+1)-Dimensional Kaup-Kupershmidt Equation. Communications in Mathematical Research . 41 (2). 103-121. doi:10.4208/cmr.2025-0008
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