Abstract
A novel systematical solution procedure of the (2+1)-dimensional Konopelchenko–Dubrovsky equation is employed on the basis of the ∂̄-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 ∂̄ 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.
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