Asymptotic behavior of solutions to the cubic coupled Schrödinger systems in one space dimension (Q286743)

The paper addresses asymptotic behavior of solutions to a one-dimensional system of nonlinear Schrödinger equations for field amplitudes \(u(x,t)\) and \(v(x,t)\), which are coupled by repulsive cubic terms (cross-phase modulation, in terms of nonlinear optics), and do not contain any self-phase-modulation terms: NEWLINE\[NEWLINE iu_t + u_{xx} =| v|^2u, NEWLINE\]NEWLINE NEWLINE\[NEWLINE iv_t + v_{xx} =| u|^2v.NEWLINE\]NEWLINE A natural outcome of evolution of a generic initial configuration is decay into small-amplitude waves, under the action of the self-defocusing nonlinearity. The paper produces rigorous estimates for the decay rates.