In this paper, with the aid of symbolic computation, we present a new method for constructing soliton solutions to nonlinear differentiM-difference equations. And we successfully solve Toda and mKdV lattice.
By using the general solutions of a new coupled Riccati equations, a direct algebraic method is described to construct doubly periodic solutions (Jacobi elliptic function solution) for the coupled nonlinear Klein-Gord...By using the general solutions of a new coupled Riccati equations, a direct algebraic method is described to construct doubly periodic solutions (Jacobi elliptic function solution) for the coupled nonlinear Klein-Gordon equations.It is shown that more doubly periodic solutions and the corresponding solitary wave solutions and trigonometric function solutions can be obtained in a unified way by this method.展开更多
A robust nonlinear control method is presented for spacecraft precise formation flying.With the constraint forces and consid-ering nonlinearity and perturbations,the problem of the formation keeping is changed to the ...A robust nonlinear control method is presented for spacecraft precise formation flying.With the constraint forces and consid-ering nonlinearity and perturbations,the problem of the formation keeping is changed to the Lagrange systems with the holonomic constraints and the differential algebraic equations (DAE).The nonlinear control laws are developed by solving the DAE.Because the traditional numerical solving methods of DAE are very sensitive to the various errors and the resulting con-trol laws are not robust in engineering application,the robust control law designed method is further developed by designing the correct coefficients to correct the errors of the formation array constraints.A numeral study simulated the robustness of this method for the various errors in the formation flying mission,including the initial errors of spacecraft formation,the reference satellite orbit determination errors,the relative perturbation forces model errors,and so on.展开更多
基金National Natural Science Foundation of China under Grant Nos.60774041 and 10671121
文摘In this paper, with the aid of symbolic computation, we present a new method for constructing soliton solutions to nonlinear differentiM-difference equations. And we successfully solve Toda and mKdV lattice.
文摘By using the general solutions of a new coupled Riccati equations, a direct algebraic method is described to construct doubly periodic solutions (Jacobi elliptic function solution) for the coupled nonlinear Klein-Gordon equations.It is shown that more doubly periodic solutions and the corresponding solitary wave solutions and trigonometric function solutions can be obtained in a unified way by this method.
基金supported by the China Postdoctoral Foundation (Grant Nos. 20080440217, 200902666)
文摘A robust nonlinear control method is presented for spacecraft precise formation flying.With the constraint forces and consid-ering nonlinearity and perturbations,the problem of the formation keeping is changed to the Lagrange systems with the holonomic constraints and the differential algebraic equations (DAE).The nonlinear control laws are developed by solving the DAE.Because the traditional numerical solving methods of DAE are very sensitive to the various errors and the resulting con-trol laws are not robust in engineering application,the robust control law designed method is further developed by designing the correct coefficients to correct the errors of the formation array constraints.A numeral study simulated the robustness of this method for the various errors in the formation flying mission,including the initial errors of spacecraft formation,the reference satellite orbit determination errors,the relative perturbation forces model errors,and so on.
