In this paper, we first employ the complex method to deritive all meromorphic solutions of an auxiliary ordinary differential equation, and then find all meromorphic exact solutions of the modified ZK equation, modifi...In this paper, we first employ the complex method to deritive all meromorphic solutions of an auxiliary ordinary differential equation, and then find all meromorphic exact solutions of the modified ZK equation, modified KdV equation, nonlinear Klein-Gordon equation and modified BBM equation. Our work shows that there exist some classes of rational solutions wr,2 （z） and simple periodic solutions ws,1 （z） which are new and are not degenerated successively to by the elliptic function solutions.展开更多
In this paper, we establish the partial Schauder estimates for the Kohn Laplace equation in the Heisenberg group based on the mean value theorem, the Taylor formula and a priori estimates for the derivatives of the Ne...In this paper, we establish the partial Schauder estimates for the Kohn Laplace equation in the Heisenberg group based on the mean value theorem, the Taylor formula and a priori estimates for the derivatives of the Newton potential.展开更多
In this article, the authors consider the collapse solutions of Cauchy problem for the nonlinear Schrdinger equation iψt + 1/2 △ ψ - 1/2 ω2|x|2ψ + |ψ|2ψ = 0, x ∈ R2, which models the Bose-Einstein condensate w...In this article, the authors consider the collapse solutions of Cauchy problem for the nonlinear Schrdinger equation iψt + 1/2 △ ψ - 1/2 ω2|x|2ψ + |ψ|2ψ = 0, x ∈ R2, which models the Bose-Einstein condensate with attractive interactions. The authors establish the lower bound of collapse rate as t → T . Furthermore, the L2-concentration property of the radially symmetric collapse solutions is obtained.展开更多
In a set of vibrating quasi-two-dimensional containers with the right-hand sidewall bent inward, three new segregation patterns have been identified experimentally including a Two-Side segregation Pattern, a Left-hand...In a set of vibrating quasi-two-dimensional containers with the right-hand sidewall bent inward, three new segregation patterns have been identified experimentally including a Two-Side segregation Pattern, a Left-hand Side segregation Pattern and a pattern where big particles aggregate to the upper left part of the container. In a container with small bending degree, either the two-side segregation pattern or the left-hand side segregation pattern is stable, which is determined by the initial distribution of particles.展开更多
For 2 〈 y 〈 min{4, n}, we consider the focusing Hartree equation iut ＋ Au ＋ （｜x｜^-γ ＊ ｜u｜2）u = O, x∈ R^n Let M[u] and E[u] denote the mass and energy, respectively, of a solution u, and Q be the ground st...For 2 〈 y 〈 min{4, n}, we consider the focusing Hartree equation iut ＋ Au ＋ （｜x｜^-γ ＊ ｜u｜2）u = O, x∈ R^n Let M[u] and E[u] denote the mass and energy, respectively, of a solution u, and Q be the ground state of - △ ＋ Q = （｜x｜^-γ ＊ ｜Q｜^2）Q. Guo and Wang [Z. Angew. Math. Phy.,2014] established a dichotomy for scattering versus blow-up for the Cauchy problem of （0,1） if M[u]^l-ScE[u]^Sc 〈 M[Q] ^1-sc E[Q] ^（sc= r-2/2）. In this paper, we consider the complementary case M[u]^1-ScE[u]^sc 〉_ M[Q]^1-sc and obtain a criteria on blow-up and global existence for the Hartree equation （0.1）.展开更多
Based on empirical data,we develop a macro model with lane width and the number of lanes.For uniform flow,the model is formulated as a couple of algebra equations and solved by analytical deduction.The results show th...Based on empirical data,we develop a macro model with lane width and the number of lanes.For uniform flow,the model is formulated as a couple of algebra equations and solved by analytical deduction.The results show that the proposed model can capture the impacts of lane width,the number of lanes and the variation of the number of lanes on uniform flow.展开更多
基金supported by the NSFC(11271090)NSF of Guangdong(S2012010010121)
文摘In this paper, we first employ the complex method to deritive all meromorphic solutions of an auxiliary ordinary differential equation, and then find all meromorphic exact solutions of the modified ZK equation, modified KdV equation, nonlinear Klein-Gordon equation and modified BBM equation. Our work shows that there exist some classes of rational solutions wr,2 （z） and simple periodic solutions ws,1 （z） which are new and are not degenerated successively to by the elliptic function solutions.
基金supported by the NSFC(11201486,11326153)supported by"the Fundamental Research Funds for the Central Universities(31541411213)"
文摘In this paper, we establish the partial Schauder estimates for the Kohn Laplace equation in the Heisenberg group based on the mean value theorem, the Taylor formula and a priori estimates for the derivatives of the Newton potential.
基金Supported by National Natural Science Foundation of China (10771151)
文摘In this article, the authors consider the collapse solutions of Cauchy problem for the nonlinear Schrdinger equation iψt + 1/2 △ ψ - 1/2 ω2|x|2ψ + |ψ|2ψ = 0, x ∈ R2, which models the Bose-Einstein condensate with attractive interactions. The authors establish the lower bound of collapse rate as t → T . Furthermore, the L2-concentration property of the radially symmetric collapse solutions is obtained.
基金Project supported by the National Natural Science Foundation of China （Grant No 10274074）, and the Australian Research Council through a Discovery Project Grant.
文摘In a set of vibrating quasi-two-dimensional containers with the right-hand sidewall bent inward, three new segregation patterns have been identified experimentally including a Two-Side segregation Pattern, a Left-hand Side segregation Pattern and a pattern where big particles aggregate to the upper left part of the container. In a container with small bending degree, either the two-side segregation pattern or the left-hand side segregation pattern is stable, which is determined by the initial distribution of particles.
基金supported by the National Natural Science Foundation of China(11371267)Sichuan Province Science Foundation for Youths(2012JQ0011)
文摘For 2 〈 y 〈 min{4, n}, we consider the focusing Hartree equation iut ＋ Au ＋ （｜x｜^-γ ＊ ｜u｜2）u = O, x∈ R^n Let M[u] and E[u] denote the mass and energy, respectively, of a solution u, and Q be the ground state of - △ ＋ Q = （｜x｜^-γ ＊ ｜Q｜^2）Q. Guo and Wang [Z. Angew. Math. Phy.,2014] established a dichotomy for scattering versus blow-up for the Cauchy problem of （0,1） if M[u]^l-ScE[u]^Sc 〈 M[Q] ^1-sc E[Q] ^（sc= r-2/2）. In this paper, we consider the complementary case M[u]^1-ScE[u]^sc 〉_ M[Q]^1-sc and obtain a criteria on blow-up and global existence for the Hartree equation （0.1）.
基金Supported by the Program for New Century Excellent Talents in University of China under Grant No NCET-08-0038the National Natural Science Foundation of China under Grant Nos 70971007 and 70901005the WA Centre of Excellence in Industrial Optimization.
文摘Based on empirical data,we develop a macro model with lane width and the number of lanes.For uniform flow,the model is formulated as a couple of algebra equations and solved by analytical deduction.The results show that the proposed model can capture the impacts of lane width,the number of lanes and the variation of the number of lanes on uniform flow.
