Solitons for the modified $(2 + 1)$-dimensional Konopelchenko–Dubrovsky equations

Abstract

In the paper, we consider the modified (2 + 1)-dimensional Konopelchenko-Dubrovsky equations which possess high order nonlinear terms. Under the aid of Maple, we derive the exact traveling wave solutions of the mKDs by the auxiliary equation approach. Under some special conditions, Jacobi elliptic function solutions, degenerated triangular function solutions, and solitons for the mKD equations are constructed. MSC: 35Q53; 35B