Functional Solutions, Multi Line Solitons and Multiple Pole Solutions of the Generalized (2+1)-Dimensional Kaup-Kupershmidt Equation (Communications in Mathematical Research, 2025)
The (2+1)-dimensional integrable generalization of the Kaup-Kupershmidt (KK) equation is solved by the inverse spectral transform method inthis paper. Several new long derivative operators $V_x,$ $V_y$ and $V_t$ and the kernelfunctions $K$ of $\overline{∂}$-problem are introduced to construct a type of general solutionof 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 equationare constructed via the $\overline{∂}$-dressing method.
Keywords: KK equation; inverse scattering transform; $\overline{∂}$-dressing method; exact solution.