(untitled) (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 in this paper. Several new long derivative operators V_x, V_y and V_t and the kernel functions K of ∂-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 ∂-dressing method.