Bäcklund transformation and Wronskian solitons for the -dimensional Nizhnik–Novikov–Veselov equations

Korteweg–de Vries-type equations are seen to describe the shallow water waves, stratified internal waves, ion-acoustic waves, plasma physics and lattice dynamics, an isotropic extension of which are the ( 2 + 1 ) -dimensional Nizhnik–Novikov–Veselov equations. Hereby, based on the Hirota bilinear method and symbolic computation, we derive the bilinear form and Bäcklund transformation for such an extension. N -soliton solutions in the Wronskian form are given, and it can be verified that the Bäcklund transformation can connect the ( N − 1 ) - and N -soliton solutions. Solitonic propagation and collision are discussed: the larger-amplitude soliton moves faster and then overtakes the smaller one. After the collisions, the solitons keep their original shapes and velocities invariant except for the phase shift. Collisions among the two and three solitons are all elastic.