New exact solutions for the (2+1)-dimensional Sawada–Kotera equation

► A new test function is proposed to construct new exact solitary solution . ► The (2+1)-dimensional Sawada–Kotera equation is employed as an example. ► New wave solutions with three different velocities and frequencies are obtained. A new test function is proposed to construct new exact solitary solution for nonlinear evolution equation. The (2+1)-dimensional Sawada–Kotera equation is employed as an example to illustrate the effectiveness of the suggested method and some new wave solutions with three different velocities and frequencies are obtained. Obviously, the method can be applied to solve other type of nonlinear evolution equations as well.