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

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Communications in Theoretical Physics 2001年第7期36卷 1-6页

作者： YAN ZhenYa XIE FuDing ZHANG HongQing department of applied mathematics Dalian University of Technology Dalian 116024 China Department of Applied Mathematics Dalian University of Technology Dalian 116024 China Department of Applied Mathematics Dalian University of Technology Dalian 116024 China

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 AblowRz's 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.

关键词： modified Boussinesq equation with the damping term, nonlinear evolution equation, symmetry reduction, integrability, solitary wave solution

STUDY ON EXACT ANALYTICAL SOLUTIONS FOR TWO SYSTEMS OF NONLINEAR EVOLUTION EQUATIONS

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applied mathematics and Mechanics(English Edition) 2001年第8期22卷 925-934页

作者： YAN Zhen-ya(闫振亚) ZHANG Hong-qing(张鸿庆) department of applied mathematics Dalian University of Technology Dalian 116024 P R China Department of Applied Mathematics Dalian University of Technology Dalian 116024 P R China

The homogeneous balance method was improved and applied to two systems Of nonlinear evolution equations. As a result, several families of exact analytic solutions are derived by some new ansatzs. These solutions contain Wang's and Zhang's results and other new types of analytical solutions, such as rational fraction solutions and periodic solutions. The way can also be applied to solve more nonlinear partial differential equations.

关键词： nonlinear evolution equations improved homogeneous balance method exact analytical solution solitary wave solution rational solution

SOLVING A CLASS OF INVERSE QP PROBLEMS BY A SMOOTHING NEWTON METHOD

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Journal of Computational mathematics 2009年第6期27卷 787-801页

作者： Xiantao Xiao Liwei Zhang department of applied mathematics Dalian University of Technology Dalian 116024 China

We consider an inverse quadratic programming （IQP） problem in which the parameters in the objective function of a given quadratic programming （QP） problem are adjusted as little as possible so that a known feasible solution becomes the optimal one. This problem can be formulated as a minimization problem with a positive semidefinite cone constraint and its dual （denoted IQD（A, b）） is a semismoothly differentiable （SC^1） convex programming problem with fewer variables than the original one. In this paper a smoothing Newton method is used for getting a Karush-Kuhn-Tucker point of IQD（A, b）. The proposed method needs to solve only one linear system per iteration and achieves quadratic convergence. Numerical experiments are reported to show that the smoothing Newton method is effective for solving this class of inverse quadratic programming problems.

关键词： Fischer-Burmeister function Smoothing Newton method Inverse optimization Quadratic programming Convergence rate.

AUTO-DARBOUX TRANSFORMATION AND EXACT SOLUTIONS OF THE BRUSSELATOR REACTION DIFFUSION MODEL

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applied mathematics and Mechanics(English Edition) 2001年第5期22卷 541-546页

作者： YAN Zhenya(闫振亚) ZHANG Hongqing(张鸿庆) department of applied mathematics Dalian University of Technology Dalian 116024 P R China Department of Applied Mathematics Dalian University of Technology Dalian 116024 P R China

Firstly, using the improved homogeneous balance method, an auto-Darboux transformation (ADT) for the Brusselator reaction diffusion model is found. Based on the ADT, several exact solutions are obtained which contain some authors' results known. Secondly, by using a series of transformations, the model is reduced into a nonlinear reaction diffusion equation and then through using sine-cosine method, more exact solutions are found which contain soliton solutions.

关键词： brusselator reaction model Darboux transformation homogeneous balance method sine-cosine method exact solution

New Matrix Lie Algebra, a Powerful Tool for Constructing Multi-component C-KdV Equation Hierarchy

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Communications in Theoretical Physics 2006年第4期45卷 587-592页

作者： YU Fa-Jun ZHANG Hong-Qing department of applied mathematics Dalian University of Technology Dalian 116024 China

A set of new multi-component matrix Lie algebra is constructed, which is devoted to obtaining a new loop algebra A^-2M. It follows that an isospectral problem is established. By making use of Tu scheme, a Liouville integrable multi-component hicrarchy of soliton equations is generated, which possesses the *** Hamiltonian structures. As its reduction cases, the multi-component C-KdV hierarchy is given. Finally, the *** integrable coupling system of C-KdV hierarchy is presented through enlarging matrix spectral problem.

关键词： matrix Lie algebra Liouville integrable integrable coupling

New Complexiton Solutions of (2+1)-Dimensional Nizhnik-Novikov-Veselov Equations

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Communications in Theoretical Physics 2006年第9期46卷 407-414页

作者： ZHANG Yuan-Yuan,~+ ZHENG Ying, ZHANG Hong-Qing department of applied mathematics, dalian university of Technology, dalian 116024, China department of applied mathematics Dalian University of Technology Dalian 116024 China

In this paper, we extend the multiple Riccati equations rational expansion method by introducing a new ansatz. Using this method, many complexiton solutions of the (2+1)-dimensional Nizhnik-Novikov-Veselov equations are obtained which include various combination of hyperbolic and trigonometric periodic function solutions, various combination of hyperbolic and rational function solutions, various combination of trigonometric periodic and rational function solutions, etc. The method can be also used to solve other nonlinear partial differential equations.

关键词： rational expansion method (2+1)-dimensional Nizhnik Novikov-Veselov equations complexiton solutions

Extended Jacobi Elliptic Function Rational Expansion Method and Its Application to （2＋1）-Dimensional Stochastic Dispersive Long Wave System

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Communications in Theoretical Physics 2007年第6期47卷 969-974页

作者： SONG Li-Na ZHANG Hong-Qing department of applied mathematics Dalian University of Technology Dalian 116024 China

In this work, by means of a generalized method and symbolic computation, we extend the Jacobi elliptic function rational expansion method to uniformly construct a series of stochastic wave solutions for stochastic evolution equations. To illustrate the effectiveness of our method, we take the （2＋ 1）-dimensional stochastic dispersive long wave system as an example. We not only have obtained some known solutions, but also have constructed some new rational formal stochastic Jacobi elliptic function solutions.

关键词： stochastic evolution equations (2+ 1)-dimensional stochastic dispersive long wave system rational formal stochastic Jacobi elliptic function solutions

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Communications in Theoretical Physics 2001年第11期36卷 513-518页

作者： YAN Zhen-Ya department of applied mathematics Dalian University of TechnologyDalian 116024China

In this paper,eight types of (1-+1)-dimensional similarity reductions which contain variable coefficient equation,are obtained for the generalized KdV equation in (2+1)-dimensional space arising from the multidimensional isospectral flows associated with the second-order scalar operators by using the direct *** addition,the cnoidal wave solution and dromion-like solution are also derived by using the reduced nonlinear ordinary differential *** (1+1) dromion obtained by Lou [***.A28 (1995) 7227] and Zhang [***.9 (2000) 1] is only a special case of our ***,some properties of the dromion-like solutions are analyzed.

关键词： generalized KdV equation,similarity reduction,Painlevé-I equation,Painlevé-II equation,cnoidal waves,dromion-like solution

Soliton-like Solutions to Wick-type Stochastic mKdV Equation

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Communications in Theoretical Physics 2005年第6X期44卷 981-986页

作者： JIANG Wu-Yout ZHANG Hong-Qing department of applied mathematics Dalian University of Technology Dalian 116024 China

In this paper, the Wick-type stochastic mKdV equation is researched. Many Wick-type stochastic solitonlike solutions are given via Hermite transformation and further generalized projective Riccati equation method.

关键词： soliton-like solutions Wick-type equation Hermite transformation generalized projective Ricati equation method