Making use of the direct method proposed by Lou et al. and symbolic computation, finite symmetry transformation groups for a （2＋ l）-dimensional cubic nonlinear Schrodinger （NLS） equation and its corresponding cyl...Making use of the direct method proposed by Lou et al. and symbolic computation, finite symmetry transformation groups for a （2＋ l）-dimensional cubic nonlinear Schrodinger （NLS） equation and its corresponding cylindrical NLS equations are presented. Nine related linear independent infinitesimal generators can be obtained from the finite symmetry transformation groups by restricting the arbitrary constants in infinitesimal forms. Some exact solutions are derived from a simple travelling wave solution.展开更多
The transverse symmetry transformations associated with the normal symmetry transformations are proposedto build the transverse constraints on the basic vertices in gauge theories.I show that,while the BRST symmetryin...The transverse symmetry transformations associated with the normal symmetry transformations are proposedto build the transverse constraints on the basic vertices in gauge theories.I show that,while the BRST symmetryin non-Abelian gauge theory QCD (Quantum Chromodynamics) leads to the Slavnov-Taylor identity for the quark-gluonvertex which constrains the longitudinal part of the vertex,the transverse symmetry transformation associated with theBRST symmetry enables to derive the transverse Slavnov-Taylor identity for the quark-gluon vertex,which constrainsthe transverse part of the quark-gluon vertex from the gauge symmetry of QCD.展开更多
Conformal invariance and a new type of conserved quantities of mechanical systems with variable mass in phase space are studied. Firstly, the definition and determining equation of conformal invariance are presented. ...Conformal invariance and a new type of conserved quantities of mechanical systems with variable mass in phase space are studied. Firstly, the definition and determining equation of conformal invariance are presented. The relationship between the conformal invariance and the Lie symmetry is given, and the necessary and sufficient condition that the conformal invarianee would be the Lie symmetry under the infinitesimal transformations is provided. Secondly, a new type of conserved quantities of the conformal invariance are obtained by using the Lie symmetry of the system. Lastly, an example is given to illustrate the application of the results.展开更多
It has been pointed out by Hall et al. [Gen. Rel. Gray. 28 （1996） 299.] that matter collineations can be defined by using three different methods. But there arises the question whether one studies matter collineati...It has been pointed out by Hall et al. [Gen. Rel. Gray. 28 （1996） 299.] that matter collineations can be defined by using three different methods. But there arises the question whether one studies matter collineations by using LεTab=0, or LεT^ab = 0 or LεT^b a=0. These alternative conditions are, of. course, not generally equivalent. This problem has been explored by applying these three definitions to general static spherically symmetric spacetimes. We compare the results with each definition.展开更多
Lie symmetry reduction of some truly ＂variable coefficient＂ wave equations which are singled out from a class of （1 ＋ 1）-dimensional variable coefficient nonlinear wave equations with respect to one and two-dimen...Lie symmetry reduction of some truly ＂variable coefficient＂ wave equations which are singled out from a class of （1 ＋ 1）-dimensional variable coefficient nonlinear wave equations with respect to one and two-dimensional algebras is carried out. Some classes of exact solutions of the investigated equations are found by means of both the reductions and some modern techniques such as additional equivalent transformations and hidden symmetries and so on. Conditional symmetries are also discussed.展开更多
The Noether and Lie symmetries as well as the conserved quantities of Hamiltonian system with fractional derivatives are es-tablished. The definitions and criteria for the fractional symmetrical transformations and qu...The Noether and Lie symmetries as well as the conserved quantities of Hamiltonian system with fractional derivatives are es-tablished. The definitions and criteria for the fractional symmetrical transformations and quasi-symmetrical transformations inthe Noether sense of Hamiltonian system are first discussed. Then, using the invariance of Hamiltonian action under the infini-tesimal transformations with respect to time, generalized coordinates and generalized momentums, the fractional Noethertheorem of the system is obtained. Further, the Lie symmetry and conserved quantity of the system are acquired. Two exam-ples are presented to illustrate the application of the results.展开更多
In this paper, we consider a system of （2＋2）-dimensional nonlinear models by using CK direct method and Hereman-Nuseir method generated by the Janlent-Miodek Hierarchy. We construct some new multiple kink and singu...In this paper, we consider a system of （2＋2）-dimensional nonlinear models by using CK direct method and Hereman-Nuseir method generated by the Janlent-Miodek Hierarchy. We construct some new multiple kink and singular kink solutions of （2＋1）-Dimensional Nonlinear Models with the aid of symbolic computation.展开更多
A coupled KdV equation is studied in this manuscript. The exact solutions, such as the periodic wave solutions and solitary wave solutions by means of the deformation and mapping approach from the solutions of the non...A coupled KdV equation is studied in this manuscript. The exact solutions, such as the periodic wave solutions and solitary wave solutions by means of the deformation and mapping approach from the solutions of the nonlinear φ4 model are given. Using the symmetry theory, the Lie point symmetries and symmetry reductions of the coupled KdV equation are presented. The results show that the coupled KdV equation possesses infinitely many symmetries and may be considered as an integrable system. Also, the Palnleve test shows the coupled KdV equation possesses Palnleve property. The Backlund transformations of the coupled KdV equation related to Palnleve property and residual symmetry are shown.展开更多
This paper mainly focuses on the front-like entire solution of a classical nonlocal dispersal equation with ignition nonlinearity. Especially, the dispersal kernel function J may not be symmetric here. The asymmetry o...This paper mainly focuses on the front-like entire solution of a classical nonlocal dispersal equation with ignition nonlinearity. Especially, the dispersal kernel function J may not be symmetric here. The asymmetry of J has a great influence on the profile of the traveling waves and the sign of the wave speeds, which further makes the properties of the entire solution more diverse. We first investigate the asymptotic behavior of the traveling wave solutions since it plays an essential role in obtaining the front-like entire solution. Due to the impact of f′(0) = 0, we can no longer use the common method which mainly depends on Ikehara theorem and bilateral Laplace transform to study the asymptotic rates of the nondecreasing traveling wave and the nonincreasing one tending to 0, respectively, so we adopt another method to investigate them. Afterwards, we establish a new entire solution and obtain its qualitative properties by constructing proper supersolution and subsolution and by classifying the sign and size of the wave speeds.展开更多
By considering the one-dimensional model for describing long, small amplitude waves in shallow water, a generalized fifth-order evolution equation named the Olver water wave （OWW） equation is investigated by virtue ...By considering the one-dimensional model for describing long, small amplitude waves in shallow water, a generalized fifth-order evolution equation named the Olver water wave （OWW） equation is investigated by virtue of some new pseudo-potential systems. By introducing the corresponding pseudo-potential systems, the authors systematically construct some generalized symmetries that consider some new smooth functions {Xiβ}β=1,2…,N^i=1,2…,n depending on a finite number of partial derivatives of the nonlocal variables vβ and a restriction i,α,β∑（ ξi/ vβ）^2＋（ ηα/ vβ）^2≠0,ie.,i,α,β∑（ ξi/ vβ）^2≠0. Furthermore, i,a,B i,a,~ the authors investigate some structures associated with the Olver water wave （AOWW） equations including Lie algebra and Darboux transformation. The results are also extended to AOWW equations such as Lax, Sawada-Kotera, Kaup-Kupershmidt, It6 and Caudrey-Dodd-Cibbon-Sawada-Kotera equations, et al. Finally, the symmetries are ap- plied to investigate the initial value problems and Darboux transformations.展开更多
The Majorana neutrino mass matrix combines information from the neutrino masses and the leptonic mixing in the flavor basis. Its invariance under some transformation matrices indicates the existence of certain residua...The Majorana neutrino mass matrix combines information from the neutrino masses and the leptonic mixing in the flavor basis. Its invariance under some transformation matrices indicates the existence of certain residual symmetry. We offer an intuitive display of the structure of the Majorana neutrino mass matrix, using the whole set of the oscillation data. The structure is revealed depending on the lightest neutrino mass. We find that there are three regions with distinct characteristics of structure. A group effect and the μ-T exchange symmetry are observed. Six types of texture non-zeros are shown. Implications for flavor models are discussed.展开更多
The Bosonized Supersymmetric Sawada–Kotera(BSSK) system is constructed by applying bosonization method to a Supersymmetric Sawada–Kotera system in this paper. The symmetries on the BSSK equations are researched and ...The Bosonized Supersymmetric Sawada–Kotera(BSSK) system is constructed by applying bosonization method to a Supersymmetric Sawada–Kotera system in this paper. The symmetries on the BSSK equations are researched and the calculation shows that the BSSK equations are invariant under the scaling transformations, the space-time translations and Galilean boosts. The one-parameter invariant subgroups and the corresponding invariant solutions are researched for the BSSK equations. Four types of reduction equations and similarity solutions are proposed. Period Cnoidal wave solutions, dark solitary wave solutions and bright solitary wave solutions of the BSSK equations are demonstrated and some evolution curves of the exact solutions are figured out.展开更多
As well known, all higher dimensional Kerr-NUT-Ads metrics with arbitrary rotation and NUT parameters in an asymptotically Ad S spacetime have a new hidden symmetry. In this paper, we show that in the near horizon,the...As well known, all higher dimensional Kerr-NUT-Ads metrics with arbitrary rotation and NUT parameters in an asymptotically Ad S spacetime have a new hidden symmetry. In this paper, we show that in the near horizon,the isometry group is enhanced to include the dilatation and special conformal transformation, and find the conformal transformation contains the cosmological constant. It is demonstrated that for near horizon extremal Kerr-NUT-Ads(NHEK-N-Ad S) only one rank-2 Killing tensor decomposes into a quadratic combination of the Killing vectors in terms of conformal group, while the others are functionally independent.展开更多
基金The project supported by K.C. Wong Magna Fund in Ningbo University, National Natural Science Foundation of China under Grant Nos. 10747141 and 10735030；Zhejiang Provincial Natural Science Foundations of China under Grant No. 605408；Ningbo Natural Science Foundation under Grant Nos. 2007A610049 and 2006A610093；National Basic Research Program of China （973 Program 2007CB814800）；Program for Changjiang Scholars and Innovative Research Team in University （IRTO734）
文摘Making use of the direct method proposed by Lou et al. and symbolic computation, finite symmetry transformation groups for a （2＋ l）-dimensional cubic nonlinear Schrodinger （NLS） equation and its corresponding cylindrical NLS equations are presented. Nine related linear independent infinitesimal generators can be obtained from the finite symmetry transformation groups by restricting the arbitrary constants in infinitesimal forms. Some exact solutions are derived from a simple travelling wave solution.
基金Supported by National Natural Science Foundation of China under Grant Nos.90303006 and 10875174
文摘The transverse symmetry transformations associated with the normal symmetry transformations are proposedto build the transverse constraints on the basic vertices in gauge theories.I show that,while the BRST symmetryin non-Abelian gauge theory QCD (Quantum Chromodynamics) leads to the Slavnov-Taylor identity for the quark-gluonvertex which constrains the longitudinal part of the vertex,the transverse symmetry transformation associated with theBRST symmetry enables to derive the transverse Slavnov-Taylor identity for the quark-gluon vertex,which constrainsthe transverse part of the quark-gluon vertex from the gauge symmetry of QCD.
基金Supported by the Graduate Students' Innovative Foundation of China University of Petrolem (East China) under Grant No.S2009-19
文摘Conformal invariance and a new type of conserved quantities of mechanical systems with variable mass in phase space are studied. Firstly, the definition and determining equation of conformal invariance are presented. The relationship between the conformal invariance and the Lie symmetry is given, and the necessary and sufficient condition that the conformal invarianee would be the Lie symmetry under the infinitesimal transformations is provided. Secondly, a new type of conserved quantities of the conformal invariance are obtained by using the Lie symmetry of the system. Lastly, an example is given to illustrate the application of the results.
基金Acknowledgments 0ne of the authors （MS） would like to thank Prof Graham S. Hall for the useful discussion on the topic.
文摘It has been pointed out by Hall et al. [Gen. Rel. Gray. 28 （1996） 299.] that matter collineations can be defined by using three different methods. But there arises the question whether one studies matter collineations by using LεTab=0, or LεT^ab = 0 or LεT^b a=0. These alternative conditions are, of. course, not generally equivalent. This problem has been explored by applying these three definitions to general static spherically symmetric spacetimes. We compare the results with each definition.
基金Supported by the National Key Basic Research Project of China under Grant No.2010CB126600the National Natural Science Foundation of China under Grant No.60873070+2 种基金Shanghai Leading Academic Discipline Project No.B114the Postdoctoral Science Foundation of China under Grant No.20090450067Shanghai Postdoctoral Science Foundation under Grant No.09R21410600
文摘Lie symmetry reduction of some truly ＂variable coefficient＂ wave equations which are singled out from a class of （1 ＋ 1）-dimensional variable coefficient nonlinear wave equations with respect to one and two-dimensional algebras is carried out. Some classes of exact solutions of the investigated equations are found by means of both the reductions and some modern techniques such as additional equivalent transformations and hidden symmetries and so on. Conditional symmetries are also discussed.
基金supported by the National Natural Science Foundation of China (Grant No. 11072218)
文摘The Noether and Lie symmetries as well as the conserved quantities of Hamiltonian system with fractional derivatives are es-tablished. The definitions and criteria for the fractional symmetrical transformations and quasi-symmetrical transformations inthe Noether sense of Hamiltonian system are first discussed. Then, using the invariance of Hamiltonian action under the infini-tesimal transformations with respect to time, generalized coordinates and generalized momentums, the fractional Noethertheorem of the system is obtained. Further, the Lie symmetry and conserved quantity of the system are acquired. Two exam-ples are presented to illustrate the application of the results.
基金Supported by the National Natural Science Foundation of China under Grant No. 10647112the Fundamental Research Funds for the Central Universities
文摘In this paper, we consider a system of （2＋2）-dimensional nonlinear models by using CK direct method and Hereman-Nuseir method generated by the Janlent-Miodek Hierarchy. We construct some new multiple kink and singular kink solutions of （2＋1）-Dimensional Nonlinear Models with the aid of symbolic computation.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11675084 and 11435005Ningbo Natural Science Foundation under Grant No.2015A610159+1 种基金granted by the Opening Project of Zhejiang Provincial Top Key Discipline of Physics Sciences in Ningbo University under Grant No.xkzwl1502sponsored by K.C.Wong Magna Fund in Ningbo University
文摘A coupled KdV equation is studied in this manuscript. The exact solutions, such as the periodic wave solutions and solitary wave solutions by means of the deformation and mapping approach from the solutions of the nonlinear φ4 model are given. Using the symmetry theory, the Lie point symmetries and symmetry reductions of the coupled KdV equation are presented. The results show that the coupled KdV equation possesses infinitely many symmetries and may be considered as an integrable system. Also, the Palnleve test shows the coupled KdV equation possesses Palnleve property. The Backlund transformations of the coupled KdV equation related to Palnleve property and residual symmetry are shown.
基金supported by National Natural Science Foundation of China(Grant Nos.11671180 and 11371179)the Fundamental Research Funds for the Central Universities(Grant No.lzujbky2016-ct12)
文摘This paper mainly focuses on the front-like entire solution of a classical nonlocal dispersal equation with ignition nonlinearity. Especially, the dispersal kernel function J may not be symmetric here. The asymmetry of J has a great influence on the profile of the traveling waves and the sign of the wave speeds, which further makes the properties of the entire solution more diverse. We first investigate the asymptotic behavior of the traveling wave solutions since it plays an essential role in obtaining the front-like entire solution. Due to the impact of f′(0) = 0, we can no longer use the common method which mainly depends on Ikehara theorem and bilateral Laplace transform to study the asymptotic rates of the nondecreasing traveling wave and the nonincreasing one tending to 0, respectively, so we adopt another method to investigate them. Afterwards, we establish a new entire solution and obtain its qualitative properties by constructing proper supersolution and subsolution and by classifying the sign and size of the wave speeds.
基金supported by the National Natural Science Foundation of China(Nos.11301527,11371361)the Fundamental Research Funds for the Central Universities(No.2013QNA41)the Construction Project of the Key Discipline of Universities in Jiangsu Province During the 12th FiveYear Plans(No.SX2013008)
文摘By considering the one-dimensional model for describing long, small amplitude waves in shallow water, a generalized fifth-order evolution equation named the Olver water wave （OWW） equation is investigated by virtue of some new pseudo-potential systems. By introducing the corresponding pseudo-potential systems, the authors systematically construct some generalized symmetries that consider some new smooth functions {Xiβ}β=1,2…,N^i=1,2…,n depending on a finite number of partial derivatives of the nonlocal variables vβ and a restriction i,α,β∑（ ξi/ vβ）^2＋（ ηα/ vβ）^2≠0,ie.,i,α,β∑（ ξi/ vβ）^2≠0. Furthermore, i,a,B i,a,~ the authors investigate some structures associated with the Olver water wave （AOWW） equations including Lie algebra and Darboux transformation. The results are also extended to AOWW equations such as Lax, Sawada-Kotera, Kaup-Kupershmidt, It6 and Caudrey-Dodd-Cibbon-Sawada-Kotera equations, et al. Finally, the symmetries are ap- plied to investigate the initial value problems and Darboux transformations.
基金supported by the National Natural Science Foundation of China(Grant Nos.11035003 and 11120101004)
文摘The Majorana neutrino mass matrix combines information from the neutrino masses and the leptonic mixing in the flavor basis. Its invariance under some transformation matrices indicates the existence of certain residual symmetry. We offer an intuitive display of the structure of the Majorana neutrino mass matrix, using the whole set of the oscillation data. The structure is revealed depending on the lightest neutrino mass. We find that there are three regions with distinct characteristics of structure. A group effect and the μ-T exchange symmetry are observed. Six types of texture non-zeros are shown. Implications for flavor models are discussed.
基金Supported by the National Natural Science Foundation of China under Grant No.11305031the Natural Science Foundation of Guangdong Province under Grant No.S2013010011546+1 种基金the Science and Technology Project Foundation of Zhongshan under Grant Nos.2013A3FC0264 and 2013A3FC0334Training Programme Foundation for Outstanding Young Teachers in Higher Education Institutions of Guangdong Province under Grant No.Yq2013205
文摘The Bosonized Supersymmetric Sawada–Kotera(BSSK) system is constructed by applying bosonization method to a Supersymmetric Sawada–Kotera system in this paper. The symmetries on the BSSK equations are researched and the calculation shows that the BSSK equations are invariant under the scaling transformations, the space-time translations and Galilean boosts. The one-parameter invariant subgroups and the corresponding invariant solutions are researched for the BSSK equations. Four types of reduction equations and similarity solutions are proposed. Period Cnoidal wave solutions, dark solitary wave solutions and bright solitary wave solutions of the BSSK equations are demonstrated and some evolution curves of the exact solutions are figured out.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11275099 and 11435006
文摘As well known, all higher dimensional Kerr-NUT-Ads metrics with arbitrary rotation and NUT parameters in an asymptotically Ad S spacetime have a new hidden symmetry. In this paper, we show that in the near horizon,the isometry group is enhanced to include the dilatation and special conformal transformation, and find the conformal transformation contains the cosmological constant. It is demonstrated that for near horizon extremal Kerr-NUT-Ads(NHEK-N-Ad S) only one rank-2 Killing tensor decomposes into a quadratic combination of the Killing vectors in terms of conformal group, while the others are functionally independent.
