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Second-order nonlinear differential operators possessing invariant subspaces of submaximal dimension

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Chinese Physics B 2011年第1期20卷 42-49页

作者：朱春蓉 College of Mathematics and Computer Science Anhui Normal University

The invariant subspace method is used to construct the explicit solution of a nonlinear evolution equation. The second-order nonlinear differential operators that possess invariant subspaces of submaximal dimension are described. There are second-order nonlinear differential operators, including cubic operators and quadratic operators, which preserve an invariant subspace of submaximal dimension. A full. description, of the second-order cubic operators with constant coefficients admitting a four-dimensional invariant subspace is given. It is shown that the maximal dimension of invaxiant subspaces preserved by a second-order cubic operator is four. Several examples are given for the construction of the exact solutions to nonlinear evolution equations with cubic nonlinearities. These solutions blow up in a finite

关键词： nonlinear evolution equations cubic operators invariant subspace method submaximal dimension blow-up solution

ON A CONSTRUCTION OF INERTIALMANIFOLDS FOR A CLASS OF SECOND ORDER IN TIME evolution equations

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Chinese Annals of Mathematics,Series B 1999年第3期20卷 271-278页

作者： WANG ZONGXIN(Institute of Mathematics, Fudan University, Shanghai 200433, China.) Institute of Mathematics Fudan University Shanghai 200433 China

Inertial manifolds for a class of second order in time dissipative equations are *** author also proves an asymptotic completeness property for the inertial manifolds and characterizes the inertial manifolds as the set of trajectories whose growth is at most of order O(e-μt ) for some p > 0. As applications, a nonlinear wave equation and a problem of nonlinear oscillations of a shallow shell are considered.

关键词： Dynamical systems Inertial manifolds nonlinear evolution equations

An Application of a Generalized Version of the Dressing Method to Integration of a Variable-Coefficient Dirac System

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Chinese Physics Letters 2010年第9期27卷 8-11页

作者：苏婷王志伟 Department of Mathematical and Physical Science Henan Institute of Engineering Zhengzhou 451191

By using the generalized version of the dressing method, we consider a Dirac system. The types of nonlinear evolution equations discussed involve the integrable variable-coefficient Dirac equation and the defocusing n... 详细信息

关键词： GENERALIZATION DIRAC equation nonlinear evolution equations VARIABLES (Mathematics) SCHRODINGER equation DIFFERENCE equations -- Numerical solutions MATHEMATICAL analysis

An extension of integrable equations related to AKNS and WKI spectral problems and their reductions

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Chinese Physics B 2018年第4期27卷 134-137页

作者： Xian-Guo Geng Yun-Yun Zhai School of Mathematics and Statistics Zhengzhou University Zhengzhou 450001 China

A novel hierarchy of integrable nonlinear evolution equations related to the combined Ablowitz–Kaup–Newell–Segur（AKNS） and Wadati–Konno–Ichikawa（WKI） spectral problems is proposed,from which the Lax pair for a corresponding negative flow and its infinite many conservation laws are ***,a reduction of this hierarchy is discussed,by which a generalized sinh-Gordon equation is derived on the basis of its negative flow.

关键词： integrable extension nonlinear evolution equations infinite conservation laws

A new expansion method of first order nonlinear ordinary differential equation with at most a sixth-degree nonlinear term and its application to mBBM model

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Chinese Physics B 2008年第2期17卷 399-402页

作者：潘军廷龚伦训 School of Science Guizhou Normal University

Based on a first order nonlinear ordinary differential equation with at most a sixth-degree nonlinear term which is extended from a type of elliptic equation, and by converting it into a new expansion form, this paper proposes a new algebraic method to construct exact solutions for nonlinear evolution equations. Being concise and straightforward, the method is applied to modified Benjamin-Bona-Mahony （mBBM） model, and some new exact solutions to the system are obtained. The algorithm is of important significance in exploring exact solutions for other nonlinear evolution equations.

关键词： nonlinear evolution equations new expansion method mBBM model exact solutions

A novel hierarchy of differential integral equations and their generalized bi-Hamiltonian structures

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Chinese Physics B 2014年第6期23卷 13-17页

作者：翟云云耿献国何国亮 School of Mathematics and Statistics Zhengzhou University School of Mathematics and Information Science Zhengzhou University of Light Industry

With the aid of the zero-curvature equation, a novel integrable hierarchy of nonlinear evolution equations associated with a 3 x 3 matrix spectral problem is proposed. By using the trace identity, the bi-Hamiltonian structures of the hierarchy are established with two skew-symmetric operators. Based on two linear spectral problems, we obtain the infinite many conservation laws of the first member in the hierarchy.

关键词： spectral problem nonlinear evolution equations bi-Hamiltonian structure conservation laws

A New Method for Constructing Travelling Wave Solutions to the modified Benjamin-Bona-Mahoney Equation

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Chinese Physics Letters 2008年第7期25卷 2339-2341页

作者：王军帽张苗张文亮张睿韩家骅 School of Physics and Material Science Anhui University Hefei 230039

We present a new method to find the exact travelling wave solutions of nonlinear evolution equations, with the aid of the symbolic computation. Based on this method, we successfully solve the modified BenjaminBona-Mahoney equation, and obtain some new solutions which can be expressed by trigonometric functions and hyperbolic functions, It is shown that the proposed method is direct, effective and can be used for many other nonlinear evolution equations in mathematical physics.

关键词： WAVE mechanics nonlinear evolution equations TRIGONOMETRY EXPONENTIAL functions

Exact Solutions of Fisher and Generalized Fisher equations with Variable Coefficients

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Acta Mathematicae Applicatae Sinica 2007年第4期23卷 563-568页

作者： Arzu ■ün Cevat Kart Department of Mathematics Faculty of SciencesAnkara University06100 Tando■an-Ankara Turkey

In this work, we consider a Fisher and generalized Fisher equations with variable coefficients. Using truncated Painleve expansions of these equations, we obtain exact solutions of these equations with a constraint on... 详细信息

关键词： nonlinear evolution equations fisher equation generalized fisher equation backlund transformation painleve property

Abundant different types of exact soliton solution to the (4+1)-dimensional Fokas and (2+1)-dimensional breaking soliton equations

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Communications in Theoretical Physics 2021年第10期73卷 64-80页

作者： Sachin Kumar Monika Niwas M S Osman M A Abdou Department of Mathematics Faculty of Mathematical SciencesUniversity of DelhiDelhi-110007India Department of Mathematics Faculty of ScienceCairo UniversityGiza 12613Egypt Department of Mathematics Faculty of Applied ScienceUmm Alqura UniversityMakkah 21955Saudi Arabia Department of Physics College of SciencesUniversity of BishaP.O.Box 344Bisha 61922Saudi Arabia Department of Physics Faculty of ScienceMansoura University35516 MansouraEgypt

The prime objective of this paper is to explore the new exact soliton solutions to the higher-dimensional nonlinear Fokas equation and(2+1)-dimensional breaking soliton equations via a generalized exponential rational function(GERF) method. Many different kinds of exact soliton solution are obtained, all of which are completely novel and have never been reported in the literature before. The dynamical behaviors of some obtained exact soliton solutions are also demonstrated by a choice of appropriate values of the free constants that aid in understanding the nonlinear complex phenomena of such equations. These exact soliton solutions are observed in the shapes of different dynamical structures of localized solitary wave solutions, singular-form solitons, single solitons,double solitons, triple solitons, bell-shaped solitons, combo singular solitons, breather-type solitons,elastic interactions between triple solitons and kink waves, and elastic interactions between diverse solitons and kink waves. Because of the reduction in symbolic computation work and the additional constructed closed-form solutions, it is observed that the suggested technique is effective, robust, and straightforward. Moreover, several other types of higher-dimensional nonlinear evolution equation can be solved using the powerful GERF technique.

关键词： nonlinear evolution equations soliton solutions exact solutions generalized exponential rational function method solitary waves