Nonlinear dynamics of complex spatio-temporal processes and systems is among the most important areas of modern fundamental and applied physics. At the Radiophysical Research Institute and then at the IAP RAS this field emerged as a branch going back to L. I. Mandel'shtam and A. A. Andronov of the Gorky (Nizhny Novgorod) school of radiophysics. Many of the modern lines of research which have been widely developed at the IAP RAS were initiated by A. V. Gaponov-Grekhov. The results obtained have led to significant progress in the understanding of fundamental nonlinear phenomena such as self-action of waves and wave collapse, solitons and self-sustained waves, dynamic chaos and turbulence, chaotic synchronization, cooperative wave-based effects in multidimensional lattice and distributed nonequilibrium systems.
The world community has widely recognized priority results of the theoretical and experimental study of the electromagnetic wave self-action phenomena, which was made by V. I. Talanov, A. G. Litvak, L. A. Ostrovsky and their disciples as early as in the 1960s and 1970s and then continued at the IAP RAS. Extensive research on the effects of spatio-temporal chaos and pattern formation in dissipative systems, which was made at the IAP RAS under the guidance of M. I. Rabinovich, played an important role in the understanding of the dynamic chaos phenomenon as one of the central objects of modern nonlinear dynamics.
The studies in this field at the IAP RAS reflect its interdisciplinary nature and include such areas as spatio-temporal dynamics of nonequilibrium neuron-like media and ensembles of coupled active elements (V. I. Nekorkin, V. G. Yakhno), Dynamic chaos and structures in hydrodynamic systems, including shear flows, turbulence, and capillary waves (S. V. Kiyashko, V. P. Reutov), eddy flows in hydrodynamics (E. I. Yakubovich, A. A. Abrashkin), laser dynamics and chaotic laser synchronization (P. A. Khandokhin, I. V. Koryukin), appearance, evolution, and interaction of localized structures of the wave field in inhomogeneous dispersive media (S. N. Vlasov, K. A. Gorshkov, V. A. Mironov, E. N. Pelinovsky, and G. M. Fraiman), and new approaches to the reconstruction of evolution operators of complex dynamic systems of different nature by direct analysis of the experimental data (A. M. Feigin).
The results of these studies find their application in various fields of modern physics and related sciences, namely, in nonlinear optics and laser physics, plasma physics, geophysical hydrodynamics, climate modeling, control theory, and elaboration of neuro-imitating information technologies and devices, as well as in the development of new methods of diagnosis and treatment of various pathologies.
- Self-action, gradient catastrophe, and wave collapse
- Solitons, breathers and localized vortices in hydrodynamics
- Spatio-temporal dynamics of nonlinear fields in dissipative nonequilibrium media
- Collective processes of activity and control in neuromorphic dynamic networks
- Models of activity of neuron-like cognitive systems
- Empirical predictive models of complex systems