The problem of solving a class of nonlinear disturbed Burgers equation is studied. Using the variational iteration method, a functional is introduced, then its variational is computed, and the iteration expansion is constructed. The soliton solutions of the approximate expansion are obtained from the corresponding equation.

The shock problems for a class of the nonlinear singularly perturbed equations is studied. Using Sinc-Galerkin method, the shock solutions of boundary value problem are constructed, the approximate solution by Newton's method is obtained.

A class of dynamical model for the nonlinear vibration of a transmission line is studied. Using the homotopy mapping method, the approximate solution with an arbitrary degree of accuracy is obtained.

The shock wave problems for a class of the nonlinear singularly perturbed equations is studied. Using indirect matching method, the shock solutions of shock wave in an interval are constructed.

A type of nonlinear combustion model is studied. Using the homotopy analysis method, the approximation solution is obtained.