Nonlinear wave structures of the soliton and vortex types in complex continuous media: Theory, simulation, applications

Abstract

This edition of the Lecture Notes of TICMI is devoted to the problems of study of nonlinear wave structures of the soliton and vortex types in complex continuous media including theory and simulation of these processes and also some applications of the results in real physical media such as space plasma and plasma of the ionosphere and magnetosphere of the Earth. The results obtained in the collaborative works of the Kazan Federal University, Russia and I. Vekua Institute of Applied Mathematics, I. Javakhishvili Tbilisi State University, Georgia are presented. Some of them were discussed on special session of the VIII Annual Meeting of the Georgian Mechanical Union dedicated to the 110th Birthday Anniversary of Ilia Vekua on September 27-29, 2017, Tbilisi, Georgia. This edition consists of two parts devoted to the nonlinear wave structures and vortical structures in complex continuous media, respectively.