We show that higher-dimensional integrable systems including the (2+1)-dimensional generalized sine-Gordon equation and the (2+1)-dimensional complex mKdV equation are associated with motions of surfaces inducedby end...We show that higher-dimensional integrable systems including the (2+1)-dimensional generalized sine-Gordon equation and the (2+1)-dimensional complex mKdV equation are associated with motions of surfaces inducedby endowing with an extra space variable to the motions of curves on S^2(R) and S^3(R).展开更多
A numerical model of two-dimensional soil water movement under surface drip irrigation condition was developed. The physical process of soil water movement is described by 2D Richards equation,and the upper boundary c...A numerical model of two-dimensional soil water movement under surface drip irrigation condition was developed. The physical process of soil water movement is described by 2D Richards equation,and the upper boundary condition is depicted by the improved moving ponded area boundary. The partial differential equation(PDE) is transformed into ordinary differential equations(ODEs) through spatial semi-discretization and numerically solved by an ordinary differential equation solver(CVODE) . The numerical and field experiments indicate the good performance of the model in terms of accuracy and efficiency. The model provides a useful tool for long-term simulation of soil water movement under surface drip irrigation. Also,the model can serve as a general 2D Richards equation solver for variably saturated soil water movement,which is named as TIVS model(Tsinghua Integrated Variably Saturated soil water movement model).展开更多
基金National Natural Science Foundation of China under Grant No.10671156the Program for New Century Excellent Talents in Universities under Grant No.NCET-04-0968
文摘We show that higher-dimensional integrable systems including the (2+1)-dimensional generalized sine-Gordon equation and the (2+1)-dimensional complex mKdV equation are associated with motions of surfaces inducedby endowing with an extra space variable to the motions of curves on S^2(R) and S^3(R).
基金supported by the "Eleventh Five-year Plan" Project (Grant No.2007BAD38B01)
文摘A numerical model of two-dimensional soil water movement under surface drip irrigation condition was developed. The physical process of soil water movement is described by 2D Richards equation,and the upper boundary condition is depicted by the improved moving ponded area boundary. The partial differential equation(PDE) is transformed into ordinary differential equations(ODEs) through spatial semi-discretization and numerically solved by an ordinary differential equation solver(CVODE) . The numerical and field experiments indicate the good performance of the model in terms of accuracy and efficiency. The model provides a useful tool for long-term simulation of soil water movement under surface drip irrigation. Also,the model can serve as a general 2D Richards equation solver for variably saturated soil water movement,which is named as TIVS model(Tsinghua Integrated Variably Saturated soil water movement model).
