Low regularity justification results for envelope approximations of nonlinear wave packets in periodic media

Article type: Research Article

Authors: Matthies, Karsten^{a; *} | Uecker, Hannes^b

Affiliations: [a] Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, United Kingdom. E-mail: k.matthies@bath.ac.uk | [b] Institut für Mathematik, Universität Oldenburg, D-26111 Oldenburg, Germany. E-mail: hannes.uecker@uni-oldenburg.de

Correspondence: [*] Corresponding author. E-mail: k.matthies@bath.ac.uk.

Abstract: We consider a cubic nonlinear wave equation with highly oscillating cubic coefficient and wave packet initial data. Using a regularization step of the initial data, we give a low regularity justification of the Nonlinear Schrödinger equation as the envelope equation.

Keywords: Klein–Gordon equation, nonlinear Schrödinger equation, justification, wave packet, highly oscillating periodic media, amplitude formalism, low regularity

DOI: 10.3233/ASY-161375

Journal: Asymptotic Analysis, vol. 99, no. 1-2, pp. 53-65, 2016