Exact solutions for KdV system equations hierarchy are obtained by using the inverse scattering transform. Exact solutions of isospectral KdV hierarchy, nonisospectral KdV hierarchies and τ-equations related to the KdV spectral problem are obtained by reduction. The interaction of two solitons...

The hierarchy of the sine-Gordon equation with self-consistent sources is derived by using the eigenfunctions of recursion operator. The bilinear form of the sine-Gordon equation with self-consistent sources is given and the N-soliton solutions are obtained through Hirota method and Wronskian...

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.

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.

Bilinear form of the nonisospectral AKNS equation is given. The N-soliton solutions and double Wronskian solution are obtained through Hirota's direct method and Wronskian technique, respectively. The nonisospectral MKdV equation and its multi-soliton solutions are presented by reducing.