Multi-variable gray spatial soliton in biased centrosymmetric two-photon photorefractive crystals

To study multi-variable gray spatial soliton in biased centrosymmetric two-photon photorefractive crystals based on the theory of gray soliton in centrosymmetric two-photon photorefractive crystals, we derived the expressions of the normalized envelope solution of the centrosymmetric two-photon multi-variable grey spatial soliton numerically and investigated the characteristics of soliton. The results show that the multi-variable gray soliton is obtained by the coupling of the multi-beams which share the same polarization, wavelength and independent of each other. When only one or two variables are involved, the multi-variable gray spatial soliton degenerates into centrosymmetric two-photon multi-variable grey spatial soliton or incoherently coupled soliton pairs. When the multi-variable gray spatial soliton propagates in biased centrosymmetric two-photon photorefractive crystals, all the components propagate stably.