Solitons for the (2Â +Â 1)-dimensional Konopelchenko-Dubrovsky equations

In this paper, we investigate the (2+1)-dimensional Konopelchenko-Dubrovsky equations. Via the Sato theory and Hirota method, we present the soliton solutions in terms of the Gram determinant which can yield the bright, depression and kink solitons. With the help of analytic and graphic analysis, we find that (1) the parallel interactions occur between the kink and depression solitons, between the two bright solitons and between the two depression solitons; (2) the oblique elastic interactions occur between the bright and depression solitons, between the two bright solitons and between the two depression solitons; (3) the oblique inelastic interactions occur between the two kink solitons, between the kink and bright solitons, between the kink and depression solitons, between the two bright solitons and between the two depression solitons.