The method of the phase plane is emploied to investigate the solitary and periodic traveling waves for a class of nonlinear dispersive partial differential equations.By using the bifurcation theory of dynamical system...The method of the phase plane is emploied to investigate the solitary and periodic traveling waves for a class of nonlinear dispersive partial differential equations.By using the bifurcation theory of dynamical systems to do qualitative analysis,all possible phase portraits in the parametric space for the traveling wave systems are obtained.It can be shown that the existence of a singular straight line in the traveling wave system is the reason why smooth solitary wave solutions converge to solitary cusp wave solution when parameters are varied.The different parameter conditions for the existence of solitary and periodic wave solutions of different kinds are rigorously determined.展开更多
According to Bohr-Sommerfeld quantization rule,an equally spaced horizon area spectrum of a static,spherically symmetric black hole was obtained under an adiabatic invariant action.This method can be extended to the r...According to Bohr-Sommerfeld quantization rule,an equally spaced horizon area spectrum of a static,spherically symmetric black hole was obtained under an adiabatic invariant action.This method can be extended to the rotating black holes.As an example,this method is applied to the rotating BTZ black hole and the quantized spectrum of the horizon area is obtained.It is shown that the area spectrum of the rotating BTZ black hole is also equally spaced and irrelevant to the rotating parameter,which is consistent with the Bekenstein conjecture.Specifically,the derivation does not need the quasinormal frequencies and the small angular momentum limit.展开更多
Circular polarization selection of light is an important property of helical micro-nanostructure.The helical thin films fabricated by glancing angle deposition can provide both circular polarization selection and wave...Circular polarization selection of light is an important property of helical micro-nanostructure.The helical thin films fabricated by glancing angle deposition can provide both circular polarization selection and wavelength tuning in this work.Their selective transmissions were depicted in calculations and experiments.The wavelength tuning mechanism was revealed as the relationship between peak wavelength and deposition parameters.Therefore,tunable circular polarization components can be designed according to the mechanism mentioned above and fabricated by glancing angle deposition techniques.Potential applications include tunable optical filters,optical pulse-shapers,biosensors etc.展开更多
基金National Natural Science Foundation of China(No.19731003,No.19961003)Yunnan Provincial Natural Science Foundation of China(No.1999A0018M,No.2000A0002M)
文摘The method of the phase plane is emploied to investigate the solitary and periodic traveling waves for a class of nonlinear dispersive partial differential equations.By using the bifurcation theory of dynamical systems to do qualitative analysis,all possible phase portraits in the parametric space for the traveling wave systems are obtained.It can be shown that the existence of a singular straight line in the traveling wave system is the reason why smooth solitary wave solutions converge to solitary cusp wave solution when parameters are varied.The different parameter conditions for the existence of solitary and periodic wave solutions of different kinds are rigorously determined.
基金supported by the National Natural Science Foundation of China(Grant Nos.10773002,10875012 and 11175019)the Fundamental Research Funds for the Central Universities(Grant No.105116)the Team Research Program of Hubei University for Nationalities(Grant No. MY2011T006)
文摘According to Bohr-Sommerfeld quantization rule,an equally spaced horizon area spectrum of a static,spherically symmetric black hole was obtained under an adiabatic invariant action.This method can be extended to the rotating black holes.As an example,this method is applied to the rotating BTZ black hole and the quantized spectrum of the horizon area is obtained.It is shown that the area spectrum of the rotating BTZ black hole is also equally spaced and irrelevant to the rotating parameter,which is consistent with the Bekenstein conjecture.Specifically,the derivation does not need the quasinormal frequencies and the small angular momentum limit.
基金the financial support of the project from the National Natural Science Foundation of China(Grant No.60977042)the Natural Science Foundation of Guangdong Provincial(Grant No.9151027501000070)
文摘Circular polarization selection of light is an important property of helical micro-nanostructure.The helical thin films fabricated by glancing angle deposition can provide both circular polarization selection and wavelength tuning in this work.Their selective transmissions were depicted in calculations and experiments.The wavelength tuning mechanism was revealed as the relationship between peak wavelength and deposition parameters.Therefore,tunable circular polarization components can be designed according to the mechanism mentioned above and fabricated by glancing angle deposition techniques.Potential applications include tunable optical filters,optical pulse-shapers,biosensors etc.
