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 - <p style="text-align: justify;">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.</p>