The propagation of the waves in periodic media at large time

Article type: Research Article

Authors: Korotyaev, Evgeni

Affiliations: Math. Dep. 2, ETU, 5 Prof. Popov Str., St. Petersburg, 197376, Russia, E-mail: evgeni@niif.spb.su

Note: [] Partially supported by a grant from INTAS and a grant from the Russian Fund of Fundamental Research.

Abstract: Asymptotic estimates at large time of the Green function to the wave equation with periodic coefficients are found. An estimate of the wave front is also obtained. It is shown that the spectral band (with number n=0,1,2,…) of the corresponding Hill operator ‘creates’ a wave having the front velocity cn < 1 . Estimates of cn in the terms of the gap lengths, the effective masses of the Hill operator are proved, both with fixed number n and their sums. Some extensions for more general cases (the Dirac operator with periodic coefficients, the Schrodinger operator with finite band potentials etc.) are also obtained.

DOI: 10.3233/ASY-1997-15101

Journal: Asymptotic Analysis, vol. 15, no. 1, pp. 1-24, 1997