New analytic solutions of two-dimensional nonlocal nonlinear media

In this paper, by using the standard symmetry reduction method, the similarity equations of two-dimensional nonlocal nonlinear optical media are obtained. Painlevé analysis is then performed for the symmetry reduction system. Moreover, test solution method is applied to the nonlocal nonlinear equation. These methods lead to some novel exact solutions of the nonlocal nonlinear optical media, including sech type soliton solutions, csch type divergent solutions, sn type period wave solutions and sn−1 type divergent solutions.