A study on the two-mode coupled modified Korteweg–de Vries using the simplified bilinear and the trigonometric-function methods

In this paper, we study the system of the two-mode coupled mKdV using the simplified bilinear method. We find the necessary conditions that make the solutions exists. In addition, we investigate the multiple soliton and multiple singular soliton solutions of this system. We find the necessary conditions to have N-soliton solutions. To verify the efficiency of our approach, we apply the trigonometric-function methods. The trigonometric-function...