A new variable coefficient algebraic method and non-travelling wave solutions of nonlinear equations

In this paper, a new auxiliary equation method is presented ofconstructing more new non-travelling wave solutions of nonlineardifferential equations in mathematical physics, which is direct andmore powerful than projective Riccati equation method. In order toillustrate the validity and the advantages of the method,(2+1)-dimensional asymmetric Nizhnik--Novikov--Vesselov equation isemployed and many new double periodic non-travelling wave solutionsare obtained. This algorithm can also be applied to other nonlineardifferential equations.