Zhang Hong-Qing

Symbolic Computation and Construction of Soliton-Like Solutions to the (2+1)-Dimensional Breaking Soliton Equation*

Based on the computerized symbolic system Maple, a new generalized expansion method of Riccati equation for constructing non-travelling wave and coefficient functions soliton-like solutions is presented by a new general ansatz. Making use of the method, we consider the (2+1)-dimensional breaking soliton equation, , and obtain rich new families of the exact solutions of the breaking soliton equation, including the non-travelling wave and constant function soliton-like solutions, singular soliton-like solutions, and triangular function solutions.

New Explicit Solitary Wave Solutions and Periodic Wave Solutions for the Generalized Coupled Hirota Satsuma KdV System

In this paper, we study the generalized coupled Hirota-Satsuma KdV system by using the new generalized transformation in homogeneous balance method. As a result, many explicit exact solutions, which contain new solitary wave solutions, periodic wave solutions, and the combined formal solitary wave solutions, and periodic wave solutions, are obtained

On a New Modified Extended Tanh-Function Method*

In this paper, a new modified extended tanh-function method is presented for constructing multiple soliton-like, periodic form and rational solutions of nonlinear evolution equations (NLEEs). This method is more powerful than the extended tanh-function method [Phys. Lett. A 277 (2000) 212] and the modified extended tanh-function method [Phys. Lett. A 299 (2002) 179]. Abundant new solutions of two physically important NLEEs are obtained by using this method and symbolic computation system Maple.

Bäcklund Transformation and Exact Solutions for a New Generalized Zakharov-Kuzentsov Equation with Nonlinear Terms of Any Order*

In this paper, with the help of symbolic computation, a new Backlund transformation (BT) for a new generalized Zakharov–Kuznetsov equation with nonlinear term of any order, , is obtained by using the homogeneous balance method. Based on the BT, some exact solutions are presented.

New Exact Travelling Wave Solutions to Hirota Equation and (1+1)-Dimensional Dispersive Long Wave Equation

Based on the computerized symbolic Maple, we study two important nonlinear evolution equations, i.e., the Hirota equation and the (1+1)-dimensional dispersive long wave equation by use of a direct and unified algebraic method named the general projective Riccati equation method to find more exact solutions to nonlinear differential equations. The method is more powerful than most of the existing tanh method. New and more general form solutions are obtained. The properties of the new formal solitary wave solutions are shown by some figures.

Symmetry Reductions, Integrability and Solitary Wave Solutions to High-Order Modified Boussinesq Equations with Damping Term*

Both the direct method due to Clarkson and Kruskal and the improved direct method due to Lou are extended to reduce the high-order modified Boussinesq equation with the damping term (HMBEDT) arising in the general Fermi–Pasta–Ulam model. As a result, several types of similarity reductions are obtained. It is easy to show that the nonlinear wave equation is not integrable under the sense of Ablowitzs conjecture from the reduction results obtained. In addition, kink-shaped solitary wave solutions, which are of important physical significance, are found for HMBEDT based on the obtained reduction equation.

New Multiple Soliton-like Solutions to (3+1)-Dimensional Burgers Equation with Variable Coefficients

A new generalized tanh function method is used for constructing exact travelling wave solutions of nonlinear partial differential equations in a unified way. The main idea of this method is to take full advantage of the Riccati equation, which has more new solutions. More new multiple soliton-like solutions are obtained for the (3+1)-dimensional Burgers equation with variable coefficients.

Extended sine-Gordon Equation Method and Its Application to Maccari's System*

An extended sine-Gordon equation method is proposed to construct exact travelling wave solutions to Maccaris equation based upon a generalized sine-Gordon equation. It is shown that more new travelling wave solutions can be found by this new method, which include bell-shaped soliton solutions, kink-shaped soliton solutions, periodic wave solution, and new travelling waves.

New Explicit Rational Solitary Wave Solutions for Discretized mKdV Lattice Equation

In this letter, we study discretized mKdV lattice equation by using a new generalized ansatz. As a result, many explicit rational exact solutions, including some new solitary wave solutions, are obtained by symbolic computation code Maple.

Auto-Bäcklund Transformation and Exact Solutions to the Generalized Kadomtsev-Petviashvili Equation with Variable Coefficients*

By using the extended homogeneous balance method, a new auto-Backlund transformation(BT) to the generalized Kadomtsev–Petviashvili equation with variable coefficients (VCGKP) are obtained. And making use of the auto-BT and choosing a special seed solution, we get many families of new exact solutions of the VCGKP equations, which include single soliton-like solutions, multi-soliton-like solutions, and special-soliton-like solutions. Since the KP equation and cylindrical KP equation are all special cases of the VCGKP equation, and the corresponding results of these equations are also given respectively.