We analyze the transverse instability of two-component spatial solitons in a saturable nonlinear medium, in relation to recent experimental observations of spatial vector solitons in photorefractive media. We present the stability analysis for all three realizations: dark-bright, bright-bright, and dark-dark soliton pairs, and demonstrate that both the nonlinearity saturation and incoherent mode interaction can lead to a strong suppression of the soliton transverse instabilities.
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Musslimani et al. (1999) studied this question.
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