The bilinear form of the non-isospectral mKdV equation is given and the exact N-soliton solutions are obtained through Hirota method and Wronskian technique, respectively.

A new loop algebra G˜M is constructed, which is devoted to establishing an isospectral problem. By making use of Tu scheme, the multi-component coupled Burgers hierarchy is obtained. Furthermore, an expanding loop algebra F˜M of the loop algebra G˜M is presented. It follows that the...

It is shown that if a new bilinear Bäcklund transformation to Boussinesq equation has been reduced by the gauge transformation, it always has another set of new N-soliton solution by performing an appropriate limiting procedure on the already known ones.