Painlevé analysis, Lie symmetries and exact solutions for (2+1)-dimensional variable coefficients Broer–Kaup equations

A (2+1) dimensional Broer–Kaup system which is obtained from the constraints of the KP equation is of importance in mathematical physics field. In this paper, the Painlevé analysis of (2+1)-variable coefficients Broer–Kaup (VCBK) equation is performed by the Weiss–Kruskal approach to check the Painlevé property. Similarity reductions of the VCBK equation to one-dimensional partial differential equations including Burger’s equation are investigated by the Lie classical method. The Lie group formalism is applied again on one of the investigated partial differential equation to derive symmetries, and the ordinary differential equations deduced from the optimal system of subalgebras are further studied and some exact solutions are obtained.

► (2+1)-Dimensional variable coefficients Broer–Kaup equations are analyzed for symmetries.
► Painlevé analysis is also performed to check integrability.
► Lie classical method is applied to investigate the symmetries.
► The (2+1) partial differential equation is reduced to ordinary differential equations.
► Some physically important exact solutions are derived.