naa a22 4500 510812449 CHVBK 20180411083449.0 cr unu---uuuuu 180411e20130701xx s 000 0 eng 10.1134/S0081543813040147 doi (NATIONALLICENCE)springer-10.1134/S0081543813040147 Homogenization and dispersion effects in the problem of propagation of waves generated by a localized source [Elektronische Daten] [V. Grushin, S. Dobrokhotov, S. Sergeev] We construct asymptotic solutions to the wave equation with velocity rapidly oscillating against a smoothly varying background and with localized initial perturbations. First, using adiabatic approximation in the operator form, we perform homogenization that leads to a linearized Boussinesq-type equation with smooth coefficients and weak "anomalous” dispersion. Then, asymptotic solutions to this and, as a consequence, to the original equations are constructed by means of a modified Maslov canonical operator; for initial perturbations of special form, these solutions are expressed in terms of combinations of products of the Airy functions of a complex argument. On the basis of explicit formulas obtained, we analyze the effect of fast oscillations of the velocity on the solution fronts and solution profiles near the front. Pleiades Publishing, Ltd., 2013 Grushin V. Moscow Institute of Electronics and Mathematics, National Research University Higher School of Economics, Bol'shoi Trekhsvyatitel'skii per. 3, 109028, Moscow, Russia aut Dobrokhotov S. Moscow Institute of Physics and Technology (State University), Institutskii per. 9, 141700, Dolgoprudnyi, Moscow oblast, Russia aut Sergeev S. Moscow Institute of Physics and Technology (State University), Institutskii per. 9, 141700, Dolgoprudnyi, Moscow oblast, Russia aut Proceedings of the Steklov Institute of Mathematics Springer US; http://www.springer-ny.com 281/1(2013-07-01), 161-178 0081-5438 281:1<161 2013 281 11501 https://doi.org/10.1134/S0081543813040147 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1134/S0081543813040147 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Grushin V. Moscow Institute of Electronics and Mathematics, National Research University Higher School of Economics, Bol'shoi Trekhsvyatitel'skii per. 3, 109028, Moscow, Russia aut NATIONALLICENCE 700 1- Dobrokhotov S. Moscow Institute of Physics and Technology (State University), Institutskii per. 9, 141700, Dolgoprudnyi, Moscow oblast, Russia aut NATIONALLICENCE 700 1- Sergeev S. Moscow Institute of Physics and Technology (State University), Institutskii per. 9, 141700, Dolgoprudnyi, Moscow oblast, Russia aut NATIONALLICENCE 773 0- Proceedings of the Steklov Institute of Mathematics Springer US; http://www.springer-ny.com 281/1(2013-07-01), 161-178 0081-5438 281:1<161 2013 281 11501 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer