The Sic-dressing method for the (2+1)-dimensional Konopelchenko-Dubrovsky equation

A novel systematical solution procedure of the (2+1)-dimensional Konopelchenko- Dubrovsky equation is employed on the basis of the partial differential over line -dressing method. The eigenfunctions and Green's function of the Lax pair play a fairly important role in constructing the scattering equation. By analyzing the analyticity of the eigenfunctions and Green's function, a new partial differential over line problem is introduced to help explore the solution with the help of Cauchy-Green formula and choosing the proper spectral transformation. Furthermore, we can work out the solution formally of the Konopelchenko-Dubrovsky equation from inverse spectral problem once the time evolution of the spectral data is determined. (C) 2022 Elsevier Ltd. All rights reserved.