The bounded and unbounded traveling wave solutions which correspond to the stable and unstable manifold at the saddle point have been worked out.

Bounded Traveling Waves of a Nonlinear Quartic Wave Equation;

The qualitative theory of ordinary differential equations and numerical simulation method are employed to investigate the bounded traveling waves of a nonlinear Boussinesq equation.

The bounded traveling waves of a nonlinear wave equation is considered,and the bifurcation theory of dynamical systems and numerical simulation method are used to analyze them qualitatively.

Exact travelling wave solutions to the Davey-Stewartson I equation;

The explicit plane travelling wave solutions to nonlinear Ur-KdV equation;

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