Wu Elimination Research Articles

Travelling wave solutions for a surface wave equation in fluid mechanics

This paper considers a non-linear wave equation arising in fluid mechanics. The exact traveling wave solutions of this equation are given by using G'/G-expansion method. This process can be reduced to solve a system of determining equations, which is large and difficult. To reduce this process, we used Wu elimination method. Example shows that this method is effective.

Exact Solution and Conservation Laws for Fifth-Order Korteweg-de Vries Equation

With the aid of Mathematica, new exact travelling wave solutions for fifth-order KdV equation are obtained by using the solitary wave ansatz method and the Wu elimination method. The derivation of conservation laws for a fifth-order KdV equation is considered.

More Exact Traveling Wave Solutions for Compound KdV Equation and MKdV Equation

Compound KdV equation and MKdV equation are investigated in the presented work, with the aid of Matlab software, using the trigonometric function transform method and the Wu elimination method, and more exact traveling wave solutions are obtained for compound KdV equation and MKdV equation.

Exact solutions and conservation laws for Ibragimov-Shabat equation which describe pseudo-spherical surface

Travelling wave solution for Ibragimov-Shabat equation, is obtained by using an improved sine-cosine method and the Wu's elimination method. An infinite number of conserved quantities for the above equation are also obtained by solving a set of coupled Riccati equations.

New algorithms for constrained dynamics based on Faddeev–Jackiw approach

In this paper, the Faddeev–Jackiw approach is improved by the Wu elimination method, so a great many complicated computations in solving constraints for the finite-dimensional polynomial-type constrained dynamics can be executed easily by using computers. Moreover, based on the Faddeev–Jackiw approach, a new algorithm of solving the constrained dynamics is presented. The new algorithm is simpler and stricter than the Faddeev–Jackiw approach. Using the new algorithm, the second Cawley counterexample is solved.

Obtaining general soliton solutions of nonlinear Boussinesq equations by trigonometric function method

A suitable transformation (trigonometric function method) is found to change nonlinear Boussinesq differential equations into nonlinear algebra equations, which are solved by Wu elimination method and therewith the general soliton solutions of Boussinesq differential equations are obtained.

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.

New explicit and exact solutions for a compound KdV-Burgers equation

In this paper, new explicit and exact solutions for a compound KdV-Burgers equation are obtained using the hyperbolic function method and the Wu elimination method, which include new solitary wave solutions and periodic solutions. Particularly important cases of the equation, such as the compound KdV, mKdV-Burgers and mKdV equations can be solved by this method. The method can also be applied to solve other nonlinear partial differential equation and equations.

Compacton solutions and multiple compacton solutions for a continuum Toda lattice model

Abstract Some special solutions of the Toda lattice model with a transversal degree of freedom are obtained. With the aid of Mathematica and Wu elimination method, more explicit solitary wave solutions, including compacton solutions, multiple compacton solutions, peakon solutions, as well as periodic solutions are found in this paper.

Exact solutions for some nonlinear evolution equations which describe pseudo-spherical surfaces

For some nonlinear evolution equations which describe pseudo-spherical surfaces two new exact solution classes are generated from known solutions: either the seed solution is constant or a traveling wave. Exact traveling wave and solitary wave solutions for Burgers’ equation and also for a fifth-order evolution equation containing the fifth-order Korteweg–de Vries equation and also the Sawada–Kotera equation, are obtained by using an improved sine–cosine method and the Wu's elimination method. We also apply Bäcklund transformations to these solutions and generate new soliton solution classes.

Applications of interval arithmetic in solving polynomial equations by Wu's elimination method

Wu's elimination method is an important method for solving multivariate polynomial equations. In this paper, we apply interval arithmetic to Wu's method and convert the problem of solving polynomial equations into that of solving interval polynomial equations. Parallel results such as zero-decomposition theorem are obtained for interval polynomial equations. The advantages of the new approach are two-folds: First, the problem of the numerical instability arisen from floating-point arithmetic is largely overcome. Second, the low efficiency of the algorithm caused by large intermediate coefficients introduced by exact compaction is dramatically improved. Some examples are provided to illustrate the effectiveness of the proposed algorithm.

Application of signal‐adapted wavelet to on‐line partial discharge measurement

AbstractThis paper develops an approach for optimal selection of signal‐adapted wavelet in de‐noising. The new method employs Wu's elimination algorithm to construct compacted orthogonal wavelets. The threshold cost function is used as the objective function during choosing of the wavelet. The approach is validated by its application to de‐noising for on‐line partial discharge (PD) measurement. The physical experiments and field tests show that the method improves the suppression of noise for on‐line PD measurement with stronger robustness. Copyright © 2004 John Wiley & Sons, Ltd.

Explicit travelling wave solutions for Zakharov equations

In this paper, several new traveling wave solutions for Zakharov equations are obtained by using bi function method and Wu elimination method, which include periodic traveling wave solutions and solitary wave solutions. Their physical meaning is also discussed.

Generalized transformations and abundant new families of exact solutions for (2 + 1)-dimensional dispersive long wave equations

A new generalized transformation based upon the well-known Riccati equation is presented and applied to find exact solutions of the (2 + 1)-dimensional dispersive long wave equation. Many explicit exact solutions are obtained that include new solitary and periodic wave solutions, and combined formal solitary and periodic wave solutions. The variant Boussinesq equation, as a special case of the (2 + 1)-dimensional dispersive long wave equation, is also solved. These exact solutions are obtained computationally using the Wu elimination method with the aid of Mathematica to solve the large system of algebraic equations produced by the solution ansatz.

Symbolic computation and observable effect for the (2 + 1)-dimensional symmetric regularized-long-wave equation from strongly magnetized cold-electron plasmas

In this paper, with the aid of computerized symbolic computation, we use the generalized hyperbolic-function method to obtain new families of exact analytic solutions for the (2 + 1)-dimensional symmetric regularized-long-wave equation. This equation describes weakly nonlinear ion-acoustic and space-charge waves in strongly magnetized cold-electron plasmas. The families we obtain consist of solitary waves and trigonometric functions. We outline an observable (2 + 1)-dimensional effect that could be of interest to future experiments on space and laboratory plasma systems. The usage of the Wu elimination method has also been addressed.

New explicit and exact travelling wave solutions for a compound KdV-Burgers equation

In this paper, new explicit and exact travelling wave solutions for a compound KdV-Burgers equation are obtained by using the hyperbola function method and the Wu elimination method, which include new solitary wave solutions and periodic solutions. Particularly important cases of the equation, such as the compound KdV, mKdV-Burgers and mKdV equations can be solved by this method. The method can also solve other nonlinear partial differential equations.

New explicit solitary wave solutions and periodic wave solutions for Whitham–Broer–Kaup equation in shallow water

Based upon the well-known Riccati equation, a new generalized transformation is presented and applied to solve Whitham–Broer–Kaup (WBK) equation in shallow water. 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. And variant Boussinesq equation and the system of approximate equation for long water waves, as the special cases of WBK equation, can also obtain the corresponding solitary wave solutions and periodic wave solutions. In addition, with the aid of Mathematica and Wu elimination method to solve a large system of algebraic equations, the course of solving equations can be carried out in computer.

Explicit and exact traveling wave solutions of Whitham–Broer–Kaup shallow water equations

In this Letter, four pairs solutions of Whitham–Broer–Kaup (WBK) equations, which contain blow-up solutions and periodic solutions, are obtained by using of hyperbolic function method, Mathematica and Wu elimination method. The method can also be applied to solve more nonlinear partial differential equation or equations.

Exact solitary wave solutions of nonlinear wave equations

The hyperbolic function method for nonlinear wave equations is presented. In support of a computer algebra system, many exact solitary wave solutions of a class of nonlinear wave equations are obtained via the method. The method is based on the fact that the solitary wave solutions are essentially of a localized nature. Writing the solitary wave solutions of a nonlinear wave equation as the polynomials of hyperbolic functions, the nonlinear wave equation can be changed into a nonlinear system of algebraic equations. The system can be solved via Wu Elimination or Grobner base method. The exact solitary wave solutions of the nonlinear wave equation are obtained including many new exact solitary wave solutions.

An Efficient Algorithm to Analyze the Power Flow Equations

In this paper Wu Elimination method was applied to study the power flow equations. In general this method can simplify a complex set of polynomial equations and analyze their solutions' structure, even when the equations have some parameters. Its role in solving polynomial equations is the same as that of Gauss Elimination method in solving linear equations. Thus all the solutions of the power flow equations can be conveniently obtained. In fact this method is a symbolic computation one and so it is robust and efficient in analyzing the polynomial equations. Results on two example power systems are provided to demonstrate its performances.