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Analytical study demonstrates exact criteria for pulse blow-up in periodic nonlinear media, highlighting how grating structure dictates spatiotemporal collapse.
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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Kivshar et al. (1994) studied this question.
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