A （2＋1）-dimensional KdV equation is obtained by use of Hirota method, which possesses N-soliton solution, specially its exact two-soliton solution is presented. By employing a proper algebraic transformation and th...A （2＋1）-dimensional KdV equation is obtained by use of Hirota method, which possesses N-soliton solution, specially its exact two-soliton solution is presented. By employing a proper algebraic transformation and the Riccati equation, a type of hell-shape soliton solutions are produced via regarding the variable in the Riccati equation as the independent variable. Finally, we extend the above （2＋1）-dimensional KdV equation into （3＋1）-dimensional equation, the two-soliton solutions are given.展开更多
Based on the primitive equations of the atmosphere,we study the effects of external forcing. dissipation and nonlinearity on the solutions of stationary motion and non-stationary motion.The results show that the asymp...Based on the primitive equations of the atmosphere,we study the effects of external forcing. dissipation and nonlinearity on the solutions of stationary motion and non-stationary motion.The results show that the asymptotic behavior of solutions of the forced dissipative nonlinear system is essentially different from that of the adiabatic non-dissipative system,the adiabatic dissipative system,the diabatic non-dissipative system and the diabatic dissipative linear system,and that the joint action of external forcing,dissipation and nonlinearity is the source of multiple equilibria. From this we can conclude that the important actions of diabatic heating and dissipation must be considered in the models of the long-term weather and the climate.展开更多
The equivalent operator equation is derived from the full primitive nonlinear equations of the atmospheric motion and the properties and physical senses of the operators are studied.In the infinite dimensional Hilbert...The equivalent operator equation is derived from the full primitive nonlinear equations of the atmospheric motion and the properties and physical senses of the operators are studied.In the infinite dimensional Hilbert space,the global asymptotic behavior of the atmosphere system with the non-stationary external forcing is studied under the assumption of the bounded external forcing.The existence theorems of the global absorbing set and the global attractor are obtained. Thus,the conclusions deduced from the large-scale atmosphere(Li and Chou 1996 a;1996 b)are extended to the general atmosphere.展开更多
The convergence problem of the family of Euler-Halley methods is considered under the Lipschitz condition with the L-average, and a united convergence theory with its applications is presented.
Based on the qualitative theory of atmospheric dynamical equations, a new method for simplifying equations, the operator constraint principle, is presented. The general rule of the method and its mathematical strictne...Based on the qualitative theory of atmospheric dynamical equations, a new method for simplifying equations, the operator constraint principle, is presented. The general rule of the method and its mathematical strictness are discussed. Moreover, the way that how to use the method to simplify equations rationally and how to get the simplified equations with harmonious and consistent dynamics is given.展开更多
基金＊The project supported by National Natural Science Foundation of China under Grant No. 10471139 and Hong Kong Research Grant Council under Grant No. HKBU/2016/03P
文摘A （2＋1）-dimensional KdV equation is obtained by use of Hirota method, which possesses N-soliton solution, specially its exact two-soliton solution is presented. By employing a proper algebraic transformation and the Riccati equation, a type of hell-shape soliton solutions are produced via regarding the variable in the Riccati equation as the independent variable. Finally, we extend the above （2＋1）-dimensional KdV equation into （3＋1）-dimensional equation, the two-soliton solutions are given.
基金This work was supported by the State Key Research Project on Dynamics and Predictive Theory of the Climate
文摘Based on the primitive equations of the atmosphere,we study the effects of external forcing. dissipation and nonlinearity on the solutions of stationary motion and non-stationary motion.The results show that the asymptotic behavior of solutions of the forced dissipative nonlinear system is essentially different from that of the adiabatic non-dissipative system,the adiabatic dissipative system,the diabatic non-dissipative system and the diabatic dissipative linear system,and that the joint action of external forcing,dissipation and nonlinearity is the source of multiple equilibria. From this we can conclude that the important actions of diabatic heating and dissipation must be considered in the models of the long-term weather and the climate.
基金The project is supported by the State Key Research Project on Dynamics and Predictive Theory of the Climate.
文摘The equivalent operator equation is derived from the full primitive nonlinear equations of the atmospheric motion and the properties and physical senses of the operators are studied.In the infinite dimensional Hilbert space,the global asymptotic behavior of the atmosphere system with the non-stationary external forcing is studied under the assumption of the bounded external forcing.The existence theorems of the global absorbing set and the global attractor are obtained. Thus,the conclusions deduced from the large-scale atmosphere(Li and Chou 1996 a;1996 b)are extended to the general atmosphere.
基金This project is supported by the Special Funds for Major State Basic Research Projects(Grant No. G19990328) the National Natural Science Foundation of China(Grant No. 10271025) also supported partly by Zhejiang Provincial Natural Science Foundation o
文摘The convergence problem of the family of Euler-Halley methods is considered under the Lipschitz condition with the L-average, and a united convergence theory with its applications is presented.
基金This work was jointly supported by the Knowledge Innovation Key Project of Chinese Academy of Sciences (Grant No. KZCX2-203) the National Key Basic Research Project (G1998040900),the National Natural Science Foundation of China (Grant Nos. 40023001, 49
文摘Based on the qualitative theory of atmospheric dynamical equations, a new method for simplifying equations, the operator constraint principle, is presented. The general rule of the method and its mathematical strictness are discussed. Moreover, the way that how to use the method to simplify equations rationally and how to get the simplified equations with harmonious and consistent dynamics is given.
