Spatiotemporal pulse collapse on periodic potentials

We present analytical results, based on the separation of different spatial scales and integral relations, which describe the spatiotemporal evolution of pulses in a nonlinear medium with periodically varying parameters (e.g., a nonlinear waveguide with a grating). Exact sufficient criteria for blow-up are formulated and the dependence of the spatiotemporal pulse collapse on the grating amplitude and period is discussed.

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