Auto-B?cklund Transformation and Similarity Reductions for the mKdV Equation with Time-Dependent Coefficient

摘要

In this chapter, an extended homogeneous balance method is used for an analytical study on time-dependent coefficient modified Korteweg-de Vries (mKdV)equation. Firstly, an auto-B?cklund transformation of the variable coefficient mKdV equation are obtained by the extended homogeneous balance method. Then, a symmetry and two conservation laws of the variable coefficient mKdV equation are given. At last, three types of similarity reductions for the variable coefficient mKdV equation are obtained. Some soliton-like solutions are also obtained from the B?cklund transformation and similarity reduction obtained above. The number of MSC: 0175.29