Chen Yu-Fu

Conservation Laws of a Class of Combined Equations

In this paper, we investigate conservation laws of a class of partial differential equations, which combines the nonlinear telegraph equations and the nonlinear diffusion-convection equations. Moreover, some special conservation laws of the combined equations are obtained by means of symmetry classifications of wave equations uxx = H(x)utt.

Classification and Approximate Solutions to a Class of Perturbed Nonlinear Wave Equations

A complete approximate symmetry classification of a class of perturbed nonlinear wave equations is performed using the method originated from Fushchich and Shtelen. Moreover, large classes of approximate invariant solutions of the equations based on the Lie group method are constructed.

Soliton Solutions to Coupled Integrable Dispersionless Equations

In this paper, by introducing a new transformation, the bilinear form of the coupled integrable dispersionless (CID) equations is derived. It will be shown that this bilinear form is easier to perform the standard Hirota process. One-, two-, and three-soliton solutions are presented. Futhermore, the N-soliton solutions are derived.

A new method to obtain approximate symmetry of nonlinear evolution equation from perturbations

A novel method for obtaining the approximate symmetry of a partial difierential equation with a small parameter is introduced. By expanding the independent variable and the dependent variable in the small parameter series, we obtain more a†uent approximate symmetries. The method is applied to two perturbed nonlinear partial difierential equations and new approximate solutions are derived.

Application of Wu elimination method to constrained dynamics

The polynomial type Lagrange equation and Hamilton equation of finite dimensional constrained dynamics were considered. A new algorithm was presented for solving constraints based on Wu elimination method. The new algorithm does not need to calculate the rank of Hessian matrix and determine the linear dependence of equations, so the steps of calculation decrease greatly. In addition, the expanding of expression occurring in the computing process is smaller. Using the symbolic computation software platform, the new algorithm can be executed in computers.

Pseudo-differential Operators and Generalized Lax Equations in Symbolic Computation

In this paper, the pseudo-differential operators and the generalized Lax equations in integrable systems are implemented in symbolic software Mathematica. A great deal of differential polynomials which appear in the procedure are dealt with by differential characteristic chain method. Using the program, several classical examples are given.

Conservation laws of the generalized short pulse equation

We show that the generalized short pulse equation is nonlinearly self-adjoint with differential substitution. Moreover, any adjoint symmetry is a differential substitution of nonlinear self-adjointness, and vice versa. Consequently, the general conservation law formula is constructed and new conservation laws for some special cases are found.