Localized solutions for linearized MHD equations and interaction of Alfven modes

A. I. Allilueva^{2, 3, 4} - A. I. Shafarevich^{1, 2, 3, 4}

¹ Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow 119899, Russia
² Moscow Institute of Physics and Technology (State University), 9 Inststitutskii per., Dolgoprudny 141700, Russia
³ A. Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, 101-1 pr. Vernadskogo, 119526 Moscow, Russia
⁴ National Research Centre "Kurchatov Institute", 1 pl. Kurchatova, 123182 Moscow, Russia

Abstract
We study the asymptotic behavior of solutions of the Cauchy problem for a linearized system of magnetohydrodynamic equations with initial conditions localized near a two-dimensional surface. Equations governing the evolution of the leading term of asymptotics are derived. Localization and growth of a small perturbation are described. Refs 11.