The novel solutions of auxiliary equation and their application to the (2 + 1)-dimensional Burgers equations

The present paper deals with families of non-trivial novel solutions of the general elliptic equation ϕ′2(ξ)=ddξϕ2=a0+a1ϕ+a2ϕ2+a3ϕ3+a4ϕ4. Based on these novel solutions, a direct and generalized algebraic algorithm is described to construct the new non-travelling wave solutions of systems of nonlinear partial differential equations (NLPDEs). Subsequently, a series of important non-travelling wave solutions of the (2 + 1)-dimensional Burgers equations are obtained.