In this paper, the Riemann–Hilbert problem of the modified Korteweg–de Vries (mKdV) equation is studied, from which a new combined soliton solution is obtained. In addition, to illustrate the dynamics of the new combined soliton solution, an algebra technique is developed to demonstrate the soliton interactions using $Mathematica$ symbolic computations. The proposed method is effective in deriving and investigating new soliton solutions of the mKdV equation. The results also expand the understanding of the soliton structure of the mKdV equation.
