title: Stability and nonlinear dynamics of solitary waves generated by subcritical oscillatory instability under the action of feedback control.
abstract: We consider the influence of global feedback control which acts on an oscillatory system governed by a subcritical Ginzburg-Landau equation. Exact solutions corresponding to solitary-wave solutions are obtained. A generalized variational approach is applied for the simplification of the whole problem and its reduction to a finite-dimensional dynamical model. The finite-dimensional evolution model is used for studying the indirect interaction between solitary waves caused by the global control. The stability analysis is held in the framework of the finite-dimensional model. The boundaries of monotonic and oscillatory instabilities are obtained. The basic types of dynamics provided by the finite-dimensional model are described and compared with the results of a direct numerical simulation of the original equation.
authors.affiliation: Department of Mathematics, Technion-Israel Institute of Technology, Haifa 32000, Israel.
authors.forename: Y
authors.initials: Y
authors.lastname: Kanevsky
authors.forename: A A
authors.initials: AA
authors.lastname: Nepomnyashchy