A two-mode modified KdV equation with multiple soliton solutions

In this work we establish a two-mode modified Korteweg-de Vries equation (TmKdV). We show that multiple soliton solutions exist for specific values of the nonlinearity and dispersion parameters of this equation. We also derive more exact solutions for other values of these parameters. We will use the simplified Hirota's method, the tanh/coth method to conduct this analysis.