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The modulational instability of nonlinearly interacting spatially incoherentStokes waves is analyzed. Starting from a pair of nonlinear Schroedingerequations, we derive a coupled set of wave-kinetic equations by using theWigner transform technique. It is shown that the partial coherence of theinteracting waves induces novel effects on the dynamics of crossing sea states.Comment: 10 pages, 8 figures, to appear in JETP Letter

Modulational instability of nonlinearly interacting incoherent sea states