A coupled variable coefficient modified KdV equation arising from a two-layer fluid system. (English) Zbl 1267.35194
Summary: A quite general coupled variable coefficient modified KdV (VCmKdV) equation in a two-layer fluid system is derived by means of the reductive perturbation method. Making use of the CK’s direct method, some similarity reductions of the coupled VCmKdV equation are obtained and their corresponding group explanations are discussed. Some exact solutions of the coupled equations are also presented.