In this paper, we investigate the global controllability of a class of n-dimensional affine nonlinear systems with n- 1 controls and constant control matrix. A necessary and sufficient condition for its global control...In this paper, we investigate the global controllability of a class of n-dimensional affine nonlinear systems with n- 1 controls and constant control matrix. A necessary and sufficient condition for its global controllability has been obtained by using the methods recently developed. Furthermore, we generalize the above result to a class of affine nonlinear systems with a block-triangular-like structure. Finally, we will give three examples to show the applications of our results.展开更多
We construct here explicitly new deformations of the Peregrine breather of order 5 with 8 real parameters.This gives new families of quasi-rational solutions of the NLS equation and thus one can describe in a more pre...We construct here explicitly new deformations of the Peregrine breather of order 5 with 8 real parameters.This gives new families of quasi-rational solutions of the NLS equation and thus one can describe in a more precise way the phenomena of appearance of multi rogue waves. With this method, we construct new patterns of different types of rogue waves. We get at the same time, the triangular configurations as well as rings isolated. Moreover, one sees appearing for certain values of the parameters, new configurations of concentric rings.展开更多
基金The research was supported by the National Natural Science Foundation of China under Grant No. 50525721, 60221301, and 60334040, and China Postdoctoral Science Foundation under Grant No. 20060390470. Acknowledgment The authors would like to thank Prof. Lei GUO for his very valuable discussions and suggestions.
文摘In this paper, we investigate the global controllability of a class of n-dimensional affine nonlinear systems with n- 1 controls and constant control matrix. A necessary and sufficient condition for its global controllability has been obtained by using the methods recently developed. Furthermore, we generalize the above result to a class of affine nonlinear systems with a block-triangular-like structure. Finally, we will give three examples to show the applications of our results.
文摘We construct here explicitly new deformations of the Peregrine breather of order 5 with 8 real parameters.This gives new families of quasi-rational solutions of the NLS equation and thus one can describe in a more precise way the phenomena of appearance of multi rogue waves. With this method, we construct new patterns of different types of rogue waves. We get at the same time, the triangular configurations as well as rings isolated. Moreover, one sees appearing for certain values of the parameters, new configurations of concentric rings.
