Novel soliton molecules, asymmetric solitons, W-shape and the breather wave solutions to the (2+1)-dimensional Konopelchenko-Dubrovsky equation

The main task of the current work is to explore some new exact solutions of the (2 + 1)-dimensional Konopelchenko-Dubrovsky equation. First, the multi-soliton solutions are extracted via the Hirota method. Then, the soliton molecules and asymmetric solitons on the different planes like (x,y)-, (x,t)- and (y,t)-planes are developed by imposing the velocity resonance conditions to the multi-soliton solutions. Moreover, the W-shape wave solutions are investigated by taking advantage of the test function method and symbolic calculation. Finally, the breather wave solutions are studied via the new homoclinic approach. The wave structures of the attained solutions are displayed graphically to unveil the nonlinear physical characteristics. The investigative solutions in this work can help us make sense of the nonlinear dynamics of the (2 + 1)-dimensional KDE better.