Hopf bifurcation in diffusive model of nonlinear optical system with matrix fourier filteringстатья
Статья опубликована в высокорейтинговом журнале
Информация о цитировании статьи получена из
Web of Science,
Scopus
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 26 июня 2019 г.
Аннотация:We consider a new formulation of the Fourier filtering problem based on the use of matrix filters instead of conventional filters-multiplicators in the framework of the periodic boundary value problem for a quasilinear diffusion equation of nonlinear optics. Our attention is mostly focused on studying the capabilities of matrix Fourier filtering as an efficient tool for constructing periodic solutions with prescribed spatial-temporal dynamics. To this end, we analyze the spectrum of the linearized operator and the possibility to localize it by choosing a matrix Fourier filter that provides the existence of the Hopf bifurcation. We also describe the structure of bifurcation solution for two important classes of filters: finite filters-multiplicators and matrix filters. We theoretically and numerically show that along with rotating waves, typical for the Hopf bifurcation with conventional filters-multiplicators, there exist waves with new nontrivial dynamics (rotating waves with nodes and pulsating structures). These waves excite as a result of the Hopf bifurcation under an appropriate choice of nondiagonal matrix Fourier filters.