To seek new infinite sequence soliton-like exact solutions to nonlinear evolution equations （NEE（s））, by developing two characteristics of construction and mechanization on auxiliary equation method, the second ki...To seek new infinite sequence soliton-like exact solutions to nonlinear evolution equations （NEE（s））, by developing two characteristics of construction and mechanization on auxiliary equation method, the second kind of elliptie equation is highly studied and new type solutions and Backlund transformation are obtained. Then （2＋ l ）-dimensional breaking soliton equation is chosen as an example and its infinite sequence soliton-like exact solutions are constructed with the help of symbolic computation system Mathematica, which include infinite sequence smooth soliton-like solutions of Jacobi elliptic type, infinite sequence compact soliton solutions of Jacobi elliptic type and infinite sequence peak soliton solutions of exponential function type and triangular function type.展开更多
By using a new method and Mathematica, the Backlund transformations for Whitham-Broer-Kaup equations (WBK) are derived. The connections between WBK equation, heat equation and Burgers equation are found, which are use...By using a new method and Mathematica, the Backlund transformations for Whitham-Broer-Kaup equations (WBK) are derived. The connections between WBK equation, heat equation and Burgers equation are found, which are used to obtain three families of solutions for WBK equations, on of which is the family of solitary wave solutions.展开更多
The modified Korteweg-de Vries （mKdV） typed equations can be used to describe certain nonlinear phenomena in fluids, plasmas, and optics. In this paper, the discretized mKdV lattice equation is investigated. With th...The modified Korteweg-de Vries （mKdV） typed equations can be used to describe certain nonlinear phenomena in fluids, plasmas, and optics. In this paper, the discretized mKdV lattice equation is investigated. With the aid of symbolic computation, the discrete matrix spectral problem for that system is constructed. Darboux transformation for that system is established based on the resulting spectral problem. Explicit solutions are derived via the Darboux transformation. Structures of those solutions are shown graphically, which might be helpful to understand some physical processes in fluids, plasmas, and optics.展开更多
A shift sampling theory established by author （1997a） is a generalization of Fourier transform computation theory. Based on this theory, I develop an Algorithm-Error （A-E） equation of potential field transformatio...A shift sampling theory established by author （1997a） is a generalization of Fourier transform computation theory. Based on this theory, I develop an Algorithm-Error （A-E） equation of potential field transformations in the wavenumber domain, which not only gives a more flexible algorithm of potential field transformations, but also reveals the law of error of potential field transformations in the wavenumber domain. The DFT0η η（0.5, 0.5） reduction-to-pole （RTP） technique derived from the A-E equation significantly improves the resolution and accuracy of RTP anomalies at low magnetic latitudes, including the magnetic equator. The law （origin, form mechanism, and essential properties） of the edge oscillation revealed by the A-E equation points out theoretically a way of improving the effect of existing padding methods in high-pass transformations in the wavenumber domain.展开更多
Using Girsanov transformation,we derive a new link from stochastic differential equations of Markovian type to nonlinear parabolic equations of Burgers-KPZ type,in such a manner that the obtained BurgersKPZ equation c...Using Girsanov transformation,we derive a new link from stochastic differential equations of Markovian type to nonlinear parabolic equations of Burgers-KPZ type,in such a manner that the obtained BurgersKPZ equation characterizes the path-independence property of the density process of Girsanov transformation for the stochastic differential equation.Our assertion also holds for SDEs on a connected differential manifold.展开更多
基金Supported by the Natural Natural Science Foundation of China under Grant No.10461006the Science Research Foundation of Institution of Higher Education of Inner Mongolia Autonomous Region,China under Grant No.NJZZ07031the Natural Science Foundation of Inner Mongolia Autonomous Region,China under Grant No.2010MS0111
文摘To seek new infinite sequence soliton-like exact solutions to nonlinear evolution equations （NEE（s））, by developing two characteristics of construction and mechanization on auxiliary equation method, the second kind of elliptie equation is highly studied and new type solutions and Backlund transformation are obtained. Then （2＋ l ）-dimensional breaking soliton equation is chosen as an example and its infinite sequence soliton-like exact solutions are constructed with the help of symbolic computation system Mathematica, which include infinite sequence smooth soliton-like solutions of Jacobi elliptic type, infinite sequence compact soliton solutions of Jacobi elliptic type and infinite sequence peak soliton solutions of exponential function type and triangular function type.
文摘By using a new method and Mathematica, the Backlund transformations for Whitham-Broer-Kaup equations (WBK) are derived. The connections between WBK equation, heat equation and Burgers equation are found, which are used to obtain three families of solutions for WBK equations, on of which is the family of solitary wave solutions.
基金Supported by the National Natural Science Foundation of China under Grant No. 60772023by the Open Fund of the State Key Laboratory of Software Development Environment under Grant No. BUAA-SKLSDE-09KF-04+2 种基金Beijing University of Aeronautics and Astronautics, by the National Basic Research Program of China (973 Program) under Grant No. 2005CB321901the Specialized Research Fund for the Doctoral Program of Higher Education under Grant Nos. 20060006024 and 200800130006Chinese Ministry of Education, and Scientific Research Common Program of Beijing Municipal Commission of Education under Grant No. KM201010772020
文摘The modified Korteweg-de Vries （mKdV） typed equations can be used to describe certain nonlinear phenomena in fluids, plasmas, and optics. In this paper, the discretized mKdV lattice equation is investigated. With the aid of symbolic computation, the discrete matrix spectral problem for that system is constructed. Darboux transformation for that system is established based on the resulting spectral problem. Explicit solutions are derived via the Darboux transformation. Structures of those solutions are shown graphically, which might be helpful to understand some physical processes in fluids, plasmas, and optics.
文摘A shift sampling theory established by author （1997a） is a generalization of Fourier transform computation theory. Based on this theory, I develop an Algorithm-Error （A-E） equation of potential field transformations in the wavenumber domain, which not only gives a more flexible algorithm of potential field transformations, but also reveals the law of error of potential field transformations in the wavenumber domain. The DFT0η η（0.5, 0.5） reduction-to-pole （RTP） technique derived from the A-E equation significantly improves the resolution and accuracy of RTP anomalies at low magnetic latitudes, including the magnetic equator. The law （origin, form mechanism, and essential properties） of the edge oscillation revealed by the A-E equation points out theoretically a way of improving the effect of existing padding methods in high-pass transformations in the wavenumber domain.
基金supported by Laboratory of Mathematics and Complex Systems,National Natural Science Foundation of China(Grant No.11131003)Specialized Research Fund for the Doctoral Program of Higher Educationthe Fundamental Research Funds for the Central Universities
文摘Using Girsanov transformation,we derive a new link from stochastic differential equations of Markovian type to nonlinear parabolic equations of Burgers-KPZ type,in such a manner that the obtained BurgersKPZ equation characterizes the path-independence property of the density process of Girsanov transformation for the stochastic differential equation.Our assertion also holds for SDEs on a connected differential manifold.
