Based on the explicit Weyl-ordered form of Wigner operator and the technique of integration within Weylordered product of operators we derive the Weyl-ordered operator product formula. The formula is then generalized ...Based on the explicit Weyl-ordered form of Wigner operator and the technique of integration within Weylordered product of operators we derive the Weyl-ordered operator product formula. The formula is then generalized to the entangled form with the help of entangled state representations.展开更多
A new general algebraic method is presented to uniformly construct a series of exact solutions for nonlinear evolution equations （NLEEs）. For illustration, we apply the new method to shallow long wave approximate eq...A new general algebraic method is presented to uniformly construct a series of exact solutions for nonlinear evolution equations （NLEEs）. For illustration, we apply the new method to shallow long wave approximate equations and successfully obtain abundant new exact solutions, which include rational solitary wave solutions and rational triangular periodic wave solutions. The method is straightforward and concise, and it can also be applied to other nonlinear evolution equations in mathematical physics.展开更多
The practice and research on the establishment of digital course environment and the reform of learning way breaks through the integration of information technology and teaching courses. Digital course environment pro...The practice and research on the establishment of digital course environment and the reform of learning way breaks through the integration of information technology and teaching courses. Digital course environment promotes the teaching interest and becomes the learning under the support of learning terminal, which must make students happy. The digitalization of teaching materials, platform of learning and learning according to requirements promotes the establishment of happy class. Establishment of learning environment is the basis of realizing the reform of learning and teaching ways. With the rapid development of information technology, intelligence learning is the necessary outcome of deep integration with education learning.展开更多
In this paper,by using bilinear form and extended homoclinic test approach,we obtain new breather-type periodic soliton solutions of the (1+1)-dimensional Sinh-Poisson equation.These results demonstrate that the nonli...In this paper,by using bilinear form and extended homoclinic test approach,we obtain new breather-type periodic soliton solutions of the (1+1)-dimensional Sinh-Poisson equation.These results demonstrate that the nonlinear evolution equation has rich dynamical behavior even if it is (1+1)-dimensional.展开更多
In the present paper, the full range Strichartz estimates for homogeneous Schroedinger equations with non-degenerate and non-smooth coefficients are proved. For inhomogeneous equation, the non-endpoint Strichartz esti...In the present paper, the full range Strichartz estimates for homogeneous Schroedinger equations with non-degenerate and non-smooth coefficients are proved. For inhomogeneous equation, the non-endpoint Strichartz estimates are also obtained.展开更多
基金The project supported by National Natural Science Foundation of China under Grant No. 10775097
文摘Based on the explicit Weyl-ordered form of Wigner operator and the technique of integration within Weylordered product of operators we derive the Weyl-ordered operator product formula. The formula is then generalized to the entangled form with the help of entangled state representations.
文摘A new general algebraic method is presented to uniformly construct a series of exact solutions for nonlinear evolution equations （NLEEs）. For illustration, we apply the new method to shallow long wave approximate equations and successfully obtain abundant new exact solutions, which include rational solitary wave solutions and rational triangular periodic wave solutions. The method is straightforward and concise, and it can also be applied to other nonlinear evolution equations in mathematical physics.
文摘The practice and research on the establishment of digital course environment and the reform of learning way breaks through the integration of information technology and teaching courses. Digital course environment promotes the teaching interest and becomes the learning under the support of learning terminal, which must make students happy. The digitalization of teaching materials, platform of learning and learning according to requirements promotes the establishment of happy class. Establishment of learning environment is the basis of realizing the reform of learning and teaching ways. With the rapid development of information technology, intelligence learning is the necessary outcome of deep integration with education learning.
基金Supported by the Natural Science Foundation of China under Grant No. 10971169Sichuan Educational Science Foundation under Grant No. 09zc008
文摘In this paper,by using bilinear form and extended homoclinic test approach,we obtain new breather-type periodic soliton solutions of the (1+1)-dimensional Sinh-Poisson equation.These results demonstrate that the nonlinear evolution equation has rich dynamical behavior even if it is (1+1)-dimensional.
基金the Graduate Student Innovation Fund of Fudan University.
文摘In the present paper, the full range Strichartz estimates for homogeneous Schroedinger equations with non-degenerate and non-smooth coefficients are proved. For inhomogeneous equation, the non-endpoint Strichartz estimates are also obtained.
