Li De-Sheng

A method for constructing exact solutions and application to Benjamin Ono equation

By using an improved projective Riccati equation method, this paper obtains several types of exact travelling wave solutions to the Benjamin Ono equation which include multiple soliton solutions, periodic soliton solutions and Weierstrass function solutions. Some of them are found for the first time. The method can be applied to other nonlinear evolution equations in mathematical physics.

Some New Exact Solutions to the Dispersive Long-Wave Equation in (2+1)-Dimensional Spaces*

In this paper, by using a further extended tanh method and symbolic computation system, some new soliton-like and period form solutions of the dispersive long-wave equation in (2+1)-dimensional spaces are obtained.

New families of non-travelling wave solutions to the (2+1)-dimensional modified dispersive water-wave system

In this paper, we introduce a further generalized projective Riccati equation method and apply it to solve the (2+1)-dimensional modified dispersive water-wave system. Many new types of non-travelling wave solutions are obtained for this system.

Exact Solutions of the (3 + 1)-Dimensional KP and KdV-Type Equations*

Abundant new soliton-like and period form solutions for certain (3 + 1)-dimensional physically important nonlinear evolution equations are obtained by using a further extended tanh method and symbolic computation system, Maple.

Solving Integrable Broer-Kaup Equations in (2+1)-Dimensional Spaces via an Improved Variable Separation Approach

Starting from Backlund transformation and using Cole-Hopf transformation, we reduce the integrable Broer-Kaup equations in (2+1)-dimensional spaces to a simple linear evolution equation with two arbitrary functions of and in this paper. And we can obtain some new solutions of the original equations by investigating the simple nonlinear evolution equation, which include the solutions obtained by the variable separation approach.

New Exact Solutions of the Integrable Broer–Kaup Equations in (2+1)-Dimensional Spaces*

In this paper, by improving some procedure of extended tanh-function method, some new exact solutions to the integrable Broer–Kaup equations in (2+1)-dimensional spaces are obtained, which include soliton-like solutions, solitary wave solutions, trigonometric function solutions, and rational solutions.