Propagation of nonlinear waves with a weak dispersion via coupled $$(2+1)$$-dimensional Konopelchenko–Dubrovsky dynamical equation

Abstract

This work applies the modified extended direct algebraic method to construct some novel exact travelling wave solutions for the coupled $$(2+1)$$ -dimensional Konopelchenko–Dubrovsky (KD) equation. Soliton, periodic, solitary wave, Jacobi elliptic function, new elliptic, Weierstrass elliptic function solutions and so on are obtained, which have several implementations in the field of applied sciences and engineering. In addition, we discuss the dynamics of some solutions like periodic, soliton and dark-singular combo soliton by their evolutionary shapes.