We use the separation of variable treatment to treat some time-dependent systems, and point out that the condition of separability is the same as the condition of existence of invariant, and the separation of variable...We use the separation of variable treatment to treat some time-dependent systems, and point out that the condition of separability is the same as the condition of existence of invariant, and the separation of variable treatment is interrelated with the quantum-invariant method and the propagator method. We directly use the separation of variable treatment to obtain the wavefunctions of the time-dependent Coulomb potential and the time-dependent Hulthén potential.展开更多
In this paper, we construct new exact solutions of the reaction-diffusion equation with time dependent variable coefficients by employing the mathematical computation via the Painleve test. We describe the behaviors a...In this paper, we construct new exact solutions of the reaction-diffusion equation with time dependent variable coefficients by employing the mathematical computation via the Painleve test. We describe the behaviors and their interactions of the obtained solutions under certain constraints and various variable coefficients.展开更多
Using classical time-average approximation, critical temperature and condensed solution in holographic pwave superconductors with a time-dependent source is investigated in probe limit. By choosing suitable gauge fiel...Using classical time-average approximation, critical temperature and condensed solution in holographic pwave superconductors with a time-dependent source is investigated in probe limit. By choosing suitable gauge field ansatz, the equation of motion for a vector field is presented. With the help of the Sturm-Liouville equation, concrete values of phase transition temperature and criticaJ frequency are obtained. It is shown that the phase transition temperature enhances as the frequency of the time-dependent source raises in high frequency regime, which means that the operators on the boundary field theory will be easier to condense.展开更多
文摘We use the separation of variable treatment to treat some time-dependent systems, and point out that the condition of separability is the same as the condition of existence of invariant, and the separation of variable treatment is interrelated with the quantum-invariant method and the propagator method. We directly use the separation of variable treatment to obtain the wavefunctions of the time-dependent Coulomb potential and the time-dependent Hulthén potential.
文摘In this paper, we construct new exact solutions of the reaction-diffusion equation with time dependent variable coefficients by employing the mathematical computation via the Painleve test. We describe the behaviors and their interactions of the obtained solutions under certain constraints and various variable coefficients.
基金Supported by the National Natural Science Foundation of China under Grant Nos. 10773002,10875012,and 11175019supported by the Fundamental Research Funds for the Central Universities under Grant No. 105116
文摘Using classical time-average approximation, critical temperature and condensed solution in holographic pwave superconductors with a time-dependent source is investigated in probe limit. By choosing suitable gauge field ansatz, the equation of motion for a vector field is presented. With the help of the Sturm-Liouville equation, concrete values of phase transition temperature and criticaJ frequency are obtained. It is shown that the phase transition temperature enhances as the frequency of the time-dependent source raises in high frequency regime, which means that the operators on the boundary field theory will be easier to condense.
