It is shown that the two-component Camassa-Holm and Hunter-Saxton systems are geometrically integrable, namely they describe pseudo-spherical surfaces. As a consequence, their infinite number of conservation laws are ...It is shown that the two-component Camassa-Holm and Hunter-Saxton systems are geometrically integrable, namely they describe pseudo-spherical surfaces. As a consequence, their infinite number of conservation laws are directly constructed. In addition, a class of nonlocal symmetries depending on the pseudo-potentials are obtained.展开更多
The axial charges of the proton and N（1440） are studied in the framework of an extended constituent quark model （CQM） including qqqqq components. The cancellation between the contributions of qqq components and qq...The axial charges of the proton and N（1440） are studied in the framework of an extended constituent quark model （CQM） including qqqqq components. The cancellation between the contributions of qqq components and qqqqq components gives a natural explanation to the experimental value of the proton axial charge, which can not be well reproduced in the traditional CQM even after the SU（6） × O（3） symmetry breaking is taken into account. The experimental value of axial charge pins down the proportion of the qqqqq component in the proton to about 20%, which is consistent with the ones given by the strong decay widths and helicity amplitudes. Besides, an axial charge for N（1440） about 1 is predicted with 30% qqqqq component, which is obtained by the strong and electromagnetic decays.展开更多
The authors construct Maurer-Cartan equation, the generating set of the differential invariant algebra and their syzygies for the symmetry groups of a （2＋1）-dimensional Burgers equation, based on the theory of equi...The authors construct Maurer-Cartan equation, the generating set of the differential invariant algebra and their syzygies for the symmetry groups of a （2＋1）-dimensional Burgers equation, based on the theory of equivariant moving frames of infinite-dimensional Lie pseudo-groups.展开更多
In this paper, Lie group classification to the N-th-order nonlinear evolution equation Ut ： UNx ＋ F（x, t, u, ux, . . . , U（N-1）x）is performed. It is shown that there are three, nine, forty-four and sixty-one ine...In this paper, Lie group classification to the N-th-order nonlinear evolution equation Ut ： UNx ＋ F（x, t, u, ux, . . . , U（N-1）x）is performed. It is shown that there are three, nine, forty-four and sixty-one inequivalent equations admitting one-, two-, three- and four-dimensionM solvable Lie algebras, respectively. We also prove that there are no semisimple Lie group 50（3） as the symmetry group of the equation, and only two realizations oral（2, R） are admitted by the equation. The resulting invariant equations contain both the well-known equations and a variety of new ones.展开更多
基金Supported by the China NSF for Distinguished Young Scholars under Grant No.10925104
文摘It is shown that the two-component Camassa-Holm and Hunter-Saxton systems are geometrically integrable, namely they describe pseudo-spherical surfaces. As a consequence, their infinite number of conservation laws are directly constructed. In addition, a class of nonlocal symmetries depending on the pseudo-potentials are obtained.
基金Support by National Natural Science Foundation of China under Grant No.10905077
文摘The axial charges of the proton and N（1440） are studied in the framework of an extended constituent quark model （CQM） including qqqqq components. The cancellation between the contributions of qqq components and qqqqq components gives a natural explanation to the experimental value of the proton axial charge, which can not be well reproduced in the traditional CQM even after the SU（6） × O（3） symmetry breaking is taken into account. The experimental value of axial charge pins down the proportion of the qqqqq component in the proton to about 20%, which is consistent with the ones given by the strong decay widths and helicity amplitudes. Besides, an axial charge for N（1440） about 1 is predicted with 30% qqqqq component, which is obtained by the strong and electromagnetic decays.
基金supported by the National Natural Science Foundation of China under Grant No.11201048the Fundamental Research Funds for the Central Universities
文摘The authors construct Maurer-Cartan equation, the generating set of the differential invariant algebra and their syzygies for the symmetry groups of a （2＋1）-dimensional Burgers equation, based on the theory of equivariant moving frames of infinite-dimensional Lie pseudo-groups.
基金supported by National Natural Science Foundation of China (Grant Nos.11001240, 10926082)the Natural Science Foundation of Zhejiang Province (Grant Nos. Y6090359, Y6090383)+1 种基金the National Natural Science Foundation for Distinguished Young Scholars of China (Grant No. 10925104)the Natural Science Foundation of Shaanxi Province (Grant No. 2009JQ1003)
文摘In this paper, Lie group classification to the N-th-order nonlinear evolution equation Ut ： UNx ＋ F（x, t, u, ux, . . . , U（N-1）x）is performed. It is shown that there are three, nine, forty-four and sixty-one inequivalent equations admitting one-, two-, three- and four-dimensionM solvable Lie algebras, respectively. We also prove that there are no semisimple Lie group 50（3） as the symmetry group of the equation, and only two realizations oral（2, R） are admitted by the equation. The resulting invariant equations contain both the well-known equations and a variety of new ones.
