Abstract: In this work, a (2+1)D Sawada-Kotera equation is studied. Based on combining Lie symmetry reduction method, perturbation Painleve truncation expansion method and homoclinic test method, the new non-traveling wave periodic solutions and the non-traveling wave kink solutions which containing a initial value perturbation parameter and an arbitrary function of time for this equation are obtained. The results may help us to understand the rich dynamic features of this equation, which will provide an powerful, efficient and easy mathematical technology to investigate more and more physical phenomena.

Key words: perturbation non-travelling wave solutions