Spatiotemporal localized solitons in cubic and power-law competing nonlinear media with different diffractions and -symmetric potentials

Analytical spatiotemporal localized soliton solutions in cubic and power-law competing nonlinear media with different diffractions and -symmetric potentials are derived. The compression and expansion of localized soliton structures in the diffraction decreasing system and periodic modulation system are studied analytically and numerically. The numerical simulation shows that exact solutions exist stable region in the defocusing cubic and focusing quintic nonlinear medium. However, exact solutions in the focusing cubic and defocusing quintic nonlinear medium are unstable, namely they cannot maintain their original shapes, they are distorted and collapse, and they ultimately decay into noise. These results might stimulate the related experiment to observe localized structures of nonlinear Schrodinger equation in -symmetric systems.