A reliable study of new nonlinear equation: Two-mode Kuramoto-Sivashinsky

In this letter, we use the sense made by Korsunsky (Phys Lett A 185:174?176, 1994 ) to establish a new nonlinear equation called the two-mode Kuramoto?Sivashinsky (TMKS). A finite series in terms of the Tanh function is proposed to be a candidate solution to this new model. Also, we study possible solutions of TMKS by means of the modified simplified bilinear method where a new Cole-Hopf transformation is considered. The new model describes the propagation of two different wave modes simultaneously.