Justification of the nonlinear Schrödinger equation in spatially periodic media
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- Busch, K., Schneider, G., Tkeshelashvili, L. et al. Z. angew. Math. Phys. (2006) 57: 905. doi:10.1007/s00033-006-0057-6
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The dynamics of the envelopes of spatially and temporarily oscillating wave packets advancing in spatially periodic media can approximately be described by solutions of a Nonlinear Schrödinger equation. Here we prove estimates for the error made by this formal approximation using Bloch wave analysis, normal form transformations, and Gronwall’s inequality.