A variety of (3 + 1)-dimensional mKdV equations derived by using the mKdV recursion operator

•We establish (3 + 1)-dimensional integrable mKdV equations.•We use the recursion operator of the mKdV equation.•We show that the new models possess distinct dispersion relations.

We establish a new variety of (3 + 1)-dimensional modified Korteweg–de Vries (mKdV) equations. The recursion operator of the mKdV equation is used to derive these higher-order dimensional integrable mKdV equations. The new integrable equations generate distinct solitons structures and distinct dispersion relations as well.