title: Control methods for localization of nonlinear waves.
abstract: A general form of a distributed feedback control algorithm based on the speed-gradient method is developed. The goal of the control is to achieve nonlinear wave localization. It is shown by example of the sine-Gordon equation that the generation and further stable propagation of a localized wave solution of a single nonlinear partial differential equation may be obtained independently of the initial conditions. The developed algorithm is extended to coupled nonlinear partial differential equations to obtain consistent localized wave solutions at rather arbitrary initial conditions.This article is part of the themed issue 'Horizons of cybernetical physics'.
authors.affiliation: Institute of Problems in Mechanical Engineering, Bolshoy 61, V.O., Saint-Petersburg 199178, Russia alexey.porubov@gmail.com.|St. Petersburg State University, 7-9, Universitetskaya nab., V.O., Saint-Petersburg 199034, Russia.|St. Petersburg State Polytechnical University, Polytechnicheskaya st., 29, Saint Petersburg 195251, Russia.
authors.forename: Alexey
authors.initials: A
authors.lastname: Porubov
authors.affiliation: Institute of Problems in Mechanical Engineering, Bolshoy 61, V.O., Saint-Petersburg 199178, Russia.|St. Petersburg State University, 7-9, Universitetskaya nab., V.O., Saint-Petersburg 199034, Russia.
authors.forename: Boris
authors.identifier: http://orcid.org/0000-0001-6323-2931
authors.initials: B
authors.lastname: Andrievsky
keywords: feedback control; nonlinear wave; numerical solution