We obtain exact spatial localized mode solutions of a(2+1)-dimensional nonlinear Schr¨odinger equation with constant diffraction and cubic-quintic nonlinearity in PT-symmetric potential, and study the linear stab...We obtain exact spatial localized mode solutions of a(2+1)-dimensional nonlinear Schr¨odinger equation with constant diffraction and cubic-quintic nonlinearity in PT-symmetric potential, and study the linear stability of these solutions. Based on these results, we further derive exact spatial localized mode solutions in a cubic-quintic medium with harmonic and PT-symmetric potentials. Moreover, the dynamical behaviors of spatial localized modes in the exponential diffraction decreasing waveguide and the periodic distributed amplification system are investigated.展开更多
Unlike in the 1D case, it is not always possible to find a minimal state-space realization for a 2D system except for some particular categories. The purpose of this paper is to explore a constructive approach to the ...Unlike in the 1D case, it is not always possible to find a minimal state-space realization for a 2D system except for some particular categories. The purpose of this paper is to explore a constructive approach to the minimal Roesser model realization problem for a class of 2D systems which does not belong to the clarified categories. As one of the main results, a constructive realization procedure is first proposed. Based on the proposed procedure, sufficient conditions and explicit construction for minimal realizations of the considered 2D systems are shown. In addition, possible variations and applications of the obtained results are discussed and illustrative examples are presented.展开更多
基金supported by the National Natural Science Foundation of China(No.22273084,No.22022305)the Open Fund of the State Key Labora-tory of Molecular Reaction Dynamics in DICP,CAS.
基金Supported by the Project of Technology Office in Zhejiang Province under Grant No.2014C32006the Special Foundation for theoretical physics Research Program of China under Grant No.11447124+1 种基金National Natural Science Foundation of China under Grant No.11374254the Higher School Visiting Scholar Development under Grant No.FX2013103
文摘We obtain exact spatial localized mode solutions of a(2+1)-dimensional nonlinear Schr¨odinger equation with constant diffraction and cubic-quintic nonlinearity in PT-symmetric potential, and study the linear stability of these solutions. Based on these results, we further derive exact spatial localized mode solutions in a cubic-quintic medium with harmonic and PT-symmetric potentials. Moreover, the dynamical behaviors of spatial localized modes in the exponential diffraction decreasing waveguide and the periodic distributed amplification system are investigated.
基金supported by the National Natural Science Foundation of China (No.60604001)Grant-in-Aid for Scientific Research from the Japan Society for the Promotion of Science (JSPS.KAKENHI 19560448)
文摘Unlike in the 1D case, it is not always possible to find a minimal state-space realization for a 2D system except for some particular categories. The purpose of this paper is to explore a constructive approach to the minimal Roesser model realization problem for a class of 2D systems which does not belong to the clarified categories. As one of the main results, a constructive realization procedure is first proposed. Based on the proposed procedure, sufficient conditions and explicit construction for minimal realizations of the considered 2D systems are shown. In addition, possible variations and applications of the obtained results are discussed and illustrative examples are presented.
