We give the generalized definitions of variable separable solutions to nonlinear evolution equations, and characterize the relation between the functional separable solution and the derivative-dependent functional sep...We give the generalized definitions of variable separable solutions to nonlinear evolution equations, and characterize the relation between the functional separable solution and the derivative-dependent functional separable solution. The new definitions can unify various kinds of variable separable solutions appearing in references. As application, we classify the generalized nonlinear diffusion equations that admit special functional separable solutions and obtain some exact solutions to the resulting equations.展开更多
In this paper, by means of the potential systems of the given nonlinear evolution equations, a procedure of symmetry preserving discretization of differential equations is presented. The specific process will be given...In this paper, by means of the potential systems of the given nonlinear evolution equations, a procedure of symmetry preserving discretization of differential equations is presented. The specific process will be given detailed in section 2. This extended method is effective for discreting the high-order (high-dimensional) nonlinear evolution equations. As examples, the invariant difference models of the mKdV equation and the Boussinesq equation are constructed.展开更多
It was demonstrated that the entanglement evolution of a specially designed quantum state in the bistochastic channel is asymmetric. In this work, we generalize the study of the quantum correlations, including entangl...It was demonstrated that the entanglement evolution of a specially designed quantum state in the bistochastic channel is asymmetric. In this work, we generalize the study of the quantum correlations, including entanglement and quantum discord, evolution asymmetry to various quantum channels. We found that the asymmetry of entanglement and quantum discord only occurs in some special quantum channels, and the behavior of the entanglement evolution may be quite different from the behavior of the quantum discord evolution. To quantum entanglement, in some channels it decreases monotonously with the increase of the quantum channel intensity. In some other channels, when we increase the intensity of the quantum channel, it decreases at first, then keeps zero for some time, and then rises up. To quantum discord, the evolution becomes more complex and you may find that it evolutes unsmoothly at some points. These results illustrate the strong dependence of the quantum correlations evolution on the property of the quantum channels.展开更多
基金The project supported by National Natural Science Foundation of China under Grant Nos.10447007 and 10671156the Natural Science Foundation of Shaanxi Province of China under Grant No.2005A13
文摘We give the generalized definitions of variable separable solutions to nonlinear evolution equations, and characterize the relation between the functional separable solution and the derivative-dependent functional separable solution. The new definitions can unify various kinds of variable separable solutions appearing in references. As application, we classify the generalized nonlinear diffusion equations that admit special functional separable solutions and obtain some exact solutions to the resulting equations.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11075055, 11275072Innovative Research Team Program of the National Natural Science Foundation of China under Grant No.61021004+2 种基金National High Technology Research and Development Program under Grant No.2011AA010101Shanghai Leading Academic Discipline Project No.B412Shanghai Knowledge Service Platform for Trustworthy Internet of Things under Grant No.ZF12131
文摘In this paper, by means of the potential systems of the given nonlinear evolution equations, a procedure of symmetry preserving discretization of differential equations is presented. The specific process will be given detailed in section 2. This extended method is effective for discreting the high-order (high-dimensional) nonlinear evolution equations. As examples, the invariant difference models of the mKdV equation and the Boussinesq equation are constructed.
基金Supported by the National Natural Science Foundation of China under Grant Nos.61327901,61490711,61225025,11474268the Fundamental Research Funds for the Central Universities under Grant No.WK2470000018
文摘It was demonstrated that the entanglement evolution of a specially designed quantum state in the bistochastic channel is asymmetric. In this work, we generalize the study of the quantum correlations, including entanglement and quantum discord, evolution asymmetry to various quantum channels. We found that the asymmetry of entanglement and quantum discord only occurs in some special quantum channels, and the behavior of the entanglement evolution may be quite different from the behavior of the quantum discord evolution. To quantum entanglement, in some channels it decreases monotonously with the increase of the quantum channel intensity. In some other channels, when we increase the intensity of the quantum channel, it decreases at first, then keeps zero for some time, and then rises up. To quantum discord, the evolution becomes more complex and you may find that it evolutes unsmoothly at some points. These results illustrate the strong dependence of the quantum correlations evolution on the property of the quantum channels.
