This paper describes an exact limit procedure by which a simple formula for the N-doublepole solution to the modified KdV equation is derived from its 2N-soliton solution in the Hirota’s form.

Sufficient conditions for the shorter curve of soliton solutions of KdV equations;

Multi-soliton solution of the Faddeev model;

Exact travelling wave solutions and concave or convex peaked and smooth soliton solutions of Camassa-Holm equation;

The known one-soliton solution in a simple parametric form is obtained by using the scattering data.

Novel multi-soliton solutions of the breaking soliton equation;

Bcklund transformation of Burgers equation by the improved homogeneous balance method was pushed out,To the above effect,general formal exact solutions,multi-soliton solutions were obtained,with thr.

The exact expression of multi-soliton solutions to the KdV-mKdV equation is obtained by Hirota method and the interaction process of multi-soliton is described by numerical figures.

Several exact soliton-like solutions for the variable coefficient KdV equation are obtained through use of the corresponding reduced NLODE.

By use of solutions of the auxiliary equation,and through making a function transformation,the new soliton-like solutions and the triangle function wave solutions to some equations are constructed with the help of symbolic computation system Mathematica.

Then the solutions of the equations istructureed by more wide assuming, and lastly we get new soliton-like solutions to the Broer-Kaup equations.

Peaked soliton solutions of shallow water wave equations on nonlinear strength;

Some solutions are obtained which include bright soliton solutions,dark soliton solutions,Jacobi elliptic function doubly periodical solutions,triangular solutions,and a new type of soliton solutions by this method.