The invariance of the differential equations under the infinitesimal transformations was used to study the Lie symmetries and conserved quantities of arbitrary order nonholonomic systems. The determining equations, th...The invariance of the differential equations under the infinitesimal transformations was used to study the Lie symmetries and conserved quantities of arbitrary order nonholonomic systems. The determining equations, the restriction equations, the structure equation and the form of the conserved quantities were obtained.展开更多
The （1＋1）-dimensional F-expansion technique and the homogeneous nonlinear balance principle have been generalized and applied for solving exact solutions to a general （3＋1）-dimensional nonlinear Schr6dinger equa...The （1＋1）-dimensional F-expansion technique and the homogeneous nonlinear balance principle have been generalized and applied for solving exact solutions to a general （3＋1）-dimensional nonlinear Schr6dinger equation （NLSE） with varying coefficients and a harmonica potential. We found that there exist two kinds of soliton solutions. The evolution features of exact solutions have been numerically studied. The （3＋1）D soliton solutions may help us to understand the nonlinear wave propagation in the nonlinear media such as classical optical waves and the matter waves of the Bose-Einstein condensates.展开更多
The method of processing of the non-stationary casual processes with the use of nonparametric methods of the theory of decisions is considered. The use of such methods is admissible in telemetry systems in need of pro...The method of processing of the non-stationary casual processes with the use of nonparametric methods of the theory of decisions is considered. The use of such methods is admissible in telemetry systems in need of processing at real rate of time of fast-changing casual processes in the conditions of aprioristic uncertainty about probabilistic properties of measured process.展开更多
We solve a generalized nonautonomous nonlinear Schrodinger equation analytically by performing the Hirota＇s bilinearization method. The precise expression of a parameter e, which provides a compatibility condition an...We solve a generalized nonautonomous nonlinear Schrodinger equation analytically by performing the Hirota＇s bilinearization method. The precise expression of a parameter e, which provides a compatibility condition and dark soliton management, is obtained. Comparing with nonautonomous bright soliton, we find that the gain parameter affects both the background and the valley of dark soliton （∈2 ≠ 1） while it has no effects on the wave central position. Moreover, the precise expressions of a nonautonomous black soliton＇s （∈2 = 1） width, background and the trajectory of its wave central, which describe the dynamic behavior of soliton＇s evolution, are investigated analytically. Finally, the stability of the dark soliton solution is demonstrated numerically. It is shown that the main characteristic of the dark solitons keeps unchanged under a slight perturbation in the compatibility condition.展开更多
文摘The invariance of the differential equations under the infinitesimal transformations was used to study the Lie symmetries and conserved quantities of arbitrary order nonholonomic systems. The determining equations, the restriction equations, the structure equation and the form of the conserved quantities were obtained.
基金Supported by National Science Foundation of China under Grant No. 2006CB921605
文摘The （1＋1）-dimensional F-expansion technique and the homogeneous nonlinear balance principle have been generalized and applied for solving exact solutions to a general （3＋1）-dimensional nonlinear Schr6dinger equation （NLSE） with varying coefficients and a harmonica potential. We found that there exist two kinds of soliton solutions. The evolution features of exact solutions have been numerically studied. The （3＋1）D soliton solutions may help us to understand the nonlinear wave propagation in the nonlinear media such as classical optical waves and the matter waves of the Bose-Einstein condensates.
文摘The method of processing of the non-stationary casual processes with the use of nonparametric methods of the theory of decisions is considered. The use of such methods is admissible in telemetry systems in need of processing at real rate of time of fast-changing casual processes in the conditions of aprioristic uncertainty about probabilistic properties of measured process.
基金Supported by the National Natural Science Foundation of China under Grant Nos. 10975180, 11047025, and 11075126 and the Applied nonlinear Science and Technology from the Most Important Among all the Top Priority Disciplines of Zhejiang Province
文摘We solve a generalized nonautonomous nonlinear Schrodinger equation analytically by performing the Hirota＇s bilinearization method. The precise expression of a parameter e, which provides a compatibility condition and dark soliton management, is obtained. Comparing with nonautonomous bright soliton, we find that the gain parameter affects both the background and the valley of dark soliton （∈2 ≠ 1） while it has no effects on the wave central position. Moreover, the precise expressions of a nonautonomous black soliton＇s （∈2 = 1） width, background and the trajectory of its wave central, which describe the dynamic behavior of soliton＇s evolution, are investigated analytically. Finally, the stability of the dark soliton solution is demonstrated numerically. It is shown that the main characteristic of the dark solitons keeps unchanged under a slight perturbation in the compatibility condition.
