We investigate the coupled inhomogeneous nonlinear Schrodinger equation by the covariant prolongationstructure theory, and obtain its Lax's representation. Moreover, we present the corresponding Riccati equations,...We investigate the coupled inhomogeneous nonlinear Schrodinger equation by the covariant prolongationstructure theory, and obtain its Lax's representation. Moreover, we present the corresponding Riccati equations, Backlundtransformation, and one-soliton solution.展开更多
We construct the integrable deformations of the Heisenberg supermagnet model with the quadratic constraints （i） S2=3S - 2I, for S ∈ USPL（2/1）/S（U（2）×U（1）） and （ii） S2=S, for S ∈ USPL（2/1）/S（L（1/...We construct the integrable deformations of the Heisenberg supermagnet model with the quadratic constraints （i） S2=3S - 2I, for S ∈ USPL（2/1）/S（U（2）×U（1）） and （ii） S2=S, for S ∈ USPL（2/1）/S（L（1/1）×U（1））. Under the gauge transformation, their corresponding gauge equivalent counterparts are derived. They are the Grassman odd and super mixed derivative nonlinear Schrodinger equation, respectively.展开更多
We present the bilinear equivalence expression of a （2＋1）-dimensional integrable equation of a classical spin system. Based on this, we construct its single-soliton solutions and two-soliton solutions by Hirota＇s ...We present the bilinear equivalence expression of a （2＋1）-dimensional integrable equation of a classical spin system. Based on this, we construct its single-soliton solutions and two-soliton solutions by Hirota＇s bilinear method. Meanwhile we show the evolution and propagation manners of two-solitons of the spin system graphically.展开更多
The Yang–Baxter equation is reinvestigated in the framework of triple system. By requiring the rational R matrix of the Yang–Baxter equation satisfying the generalized Filippov condition, we derive a relation with r...The Yang–Baxter equation is reinvestigated in the framework of triple system. By requiring the rational R matrix of the Yang–Baxter equation satisfying the generalized Filippov condition, we derive a relation with respect to the rational R matrix. Moreover the case of the super Yang–Baxter equation is also investigated.展开更多
We consider the three-dimensional compressible Navier-Stokes-Poisson system where the electric field of the internal electrostatic potential force is governed by the self-consistent Poisson equation.If the Fourier mod...We consider the three-dimensional compressible Navier-Stokes-Poisson system where the electric field of the internal electrostatic potential force is governed by the self-consistent Poisson equation.If the Fourier modes of the initial data are degenerate at the low frequency or the initial data decay fast at spatial infinity,we show that the density converges to its equilibrium state at the L 2-rate (1+t)(-7/4) or L ∞-rate (1+t)(-5/2),and the momentum decays at the L 2-rate (1+t)(-5/4) or L ∞-rate (1+t)(-2).These convergence rates are shown to be optimal for the compressible Navier-Stokes-Poisson system.展开更多
Based on the covariant prolongation structure technique,we construct the integrable higher-order deformations of the(2+1)-dimensional Heisenberg ferromagnet model and obtain their su(2) × R(λ) prolongation struc...Based on the covariant prolongation structure technique,we construct the integrable higher-order deformations of the(2+1)-dimensional Heisenberg ferromagnet model and obtain their su(2) × R(λ) prolongation structures.By associating these deformed multidimensional Heisenberg ferromagnet models with the moving space curve in Euclidean space and using the Hasimoto function,we derive their geometrical equivalent counterparts,i.e.,higher-order(2+1)-dimensional nonlinear Schrdinger equations.展开更多
In this paper, both the standard finite element discretization and a two-scale finite element discretization for SchrSdinger equations are studied. The numerical analysis is based on the regularity that is also obtain...In this paper, both the standard finite element discretization and a two-scale finite element discretization for SchrSdinger equations are studied. The numerical analysis is based on the regularity that is also obtained in this paper for the Schroedinger equations. Very satisfying applications to electronic structure computations are provided, too.展开更多
Let f ： M→ M be a self-map of a closed manifold M of dimension dim M ≥ 3. The Nielsen number N（f） of f is equal to the minimal number of fixed points of f＇ among all self-maps f＇ in the homotopy class of f. In ...Let f ： M→ M be a self-map of a closed manifold M of dimension dim M ≥ 3. The Nielsen number N（f） of f is equal to the minimal number of fixed points of f＇ among all self-maps f＇ in the homotopy class of f. In this paper, we determine N（f） for all self-maps f when M is a closed 3-manifold with S^2× R geometry. The calculation of N（f） relies on the induced homomorphisms of f on the fundamental group and on the second homotopy group of M.展开更多
基金Supported by Beijing Jiao-Wei Key Project KZ200810028013the Natural Science Foundation of China under Grant No. 10871135
文摘We investigate the coupled inhomogeneous nonlinear Schrodinger equation by the covariant prolongationstructure theory, and obtain its Lax's representation. Moreover, we present the corresponding Riccati equations, Backlundtransformation, and one-soliton solution.
基金Supported by National Key Basic Research Project of China under Grant No.2006CB805905National Natural Science Foundation of China under Grant Nos.10975102 and 10871135
文摘We construct the integrable deformations of the Heisenberg supermagnet model with the quadratic constraints （i） S2=3S - 2I, for S ∈ USPL（2/1）/S（U（2）×U（1）） and （ii） S2=S, for S ∈ USPL（2/1）/S（L（1/1）×U（1））. Under the gauge transformation, their corresponding gauge equivalent counterparts are derived. They are the Grassman odd and super mixed derivative nonlinear Schrodinger equation, respectively.
基金Supported by National Basic Research Program of China under Grant No 2004CB318000, Beijing Jiao-Wei Key Project （KZ200810028013）, and the National Natural Science Foundation of China under Grant No 10871135.
文摘We present the bilinear equivalence expression of a （2＋1）-dimensional integrable equation of a classical spin system. Based on this, we construct its single-soliton solutions and two-soliton solutions by Hirota＇s bilinear method. Meanwhile we show the evolution and propagation manners of two-solitons of the spin system graphically.
基金Supported by National Natural Science Foundation of China under Grant Nos.11375119 and 11031005Beijing Municipal Commission of Education under Grant No.KZ201210028032
文摘The Yang–Baxter equation is reinvestigated in the framework of triple system. By requiring the rational R matrix of the Yang–Baxter equation satisfying the generalized Filippov condition, we derive a relation with respect to the rational R matrix. Moreover the case of the super Yang–Baxter equation is also investigated.
基金partially supported by National Natural Science Foundation of China(Grant Nos.10871134,11011130029)the Huo Ying Dong Foundation (Grant No.111033)+3 种基金the Funding Project for Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality (Grant No.PHR201006107)partially supported by National Natural Science Foundation of China (Grant Nos.10871175,10931007,10901137)Zhejiang Provincial Natural Science Foundation of China (Grant No.Z6100217)Specialized Research Fund for the Doctoral Program of Higher Education (Grant No.20090101120005)
文摘We consider the three-dimensional compressible Navier-Stokes-Poisson system where the electric field of the internal electrostatic potential force is governed by the self-consistent Poisson equation.If the Fourier modes of the initial data are degenerate at the low frequency or the initial data decay fast at spatial infinity,we show that the density converges to its equilibrium state at the L 2-rate (1+t)(-7/4) or L ∞-rate (1+t)(-5/2),and the momentum decays at the L 2-rate (1+t)(-5/4) or L ∞-rate (1+t)(-2).These convergence rates are shown to be optimal for the compressible Navier-Stokes-Poisson system.
基金Supported by National Natural Science Foundation of China under Grant Nos. 10975102 and 11031005Beijing Municipal Commission of Education under Grant No. KZ201210028032
文摘Based on the covariant prolongation structure technique,we construct the integrable higher-order deformations of the(2+1)-dimensional Heisenberg ferromagnet model and obtain their su(2) × R(λ) prolongation structures.By associating these deformed multidimensional Heisenberg ferromagnet models with the moving space curve in Euclidean space and using the Hasimoto function,we derive their geometrical equivalent counterparts,i.e.,higher-order(2+1)-dimensional nonlinear Schrdinger equations.
基金the National Science Founda-tion of China under grant 10425105the National Basic Research Program under grant 2005CB321704
文摘In this paper, both the standard finite element discretization and a two-scale finite element discretization for SchrSdinger equations are studied. The numerical analysis is based on the regularity that is also obtained in this paper for the Schroedinger equations. Very satisfying applications to electronic structure computations are provided, too.
基金supported in part by Projeto Tematico Topologia Algebrica Geometrica e Differencial2008/57607-6supported in part by NSFC(Grant No.10931005)project of Beijing Municipal Education Commission(Grant No.KZ201310028030)
文摘Let f ： M→ M be a self-map of a closed manifold M of dimension dim M ≥ 3. The Nielsen number N（f） of f is equal to the minimal number of fixed points of f＇ among all self-maps f＇ in the homotopy class of f. In this paper, we determine N（f） for all self-maps f when M is a closed 3-manifold with S^2× R geometry. The calculation of N（f） relies on the induced homomorphisms of f on the fundamental group and on the second homotopy group of M.
