Nonlinear Interactions of Three Wave Packets in an Inhomogeneous Medium

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Abstract
Solutions for the nonlinear evolution of the one-dimensional space-time and two-dimensional steady-state interaction of three wave packets in an inhomogeneous medium are presented. A transformation of the nonlinear equations allows the use of an inverse scattering transform for finding exact time-asymptotic properties of the interaction. Inhomogeneity gives a decreased action transfer in both decay and backscattering, and suppresses explosive instabilities and soliton decay above a certain threshold.