(2+1)-Dimensional Spatial Localized Modes in Cubic-Quintic Nonlinear Media with the -Symmetric Potentials* *Supported by the Project of Technology Office in Zhejiang Province under Grant No. 2014C32006, the Special Foundation for theoretical physics Research Program of China under Grant No. 11447124, National Natural Science Foundation of China under Grant No. 11374254 and the Higher School Visiting Scholar Development under Grant No.

Abstract

We obtain exact spatial localized mode solutions of a (2+1)-dimensional nonlinear Schrödinger equation with constant diffraction and cubic-quintic nonlinearity in -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 -symmetric potentials. Moreover, the dynamical behaviors of spatial localized modes in the exponential diffraction decreasing waveguide and the periodic distributed amplification system are investigated.