Similarity Reduction of The Variable-coefficient mKdV Equation

We use the CK direct method to study a class of variable-coefficient mKdV equations, which deviate the variable coefficient differential equations are converted to ordinary differential equations. As far as we know, no researchers have used this method to study the variable-coefficient mKdV equation in the current literature. The classical Lie group method is only suitable for special forms of g(t) , h(t) , but the CK direct method we use is not only suitable for special forms, but also for general Variable-coefficient mKdV equations. Further, in order to compare whether the reduction results obtained using the two methods are consistent, we use the classical Lie group method and the CK direct method to study the variable-coefficient mKdV equation for a particular g(t) , h(t) . Finally, the results are consistent, which also confirms the correctness of CK direct method.