Speciality:
01.02.05 (Mechanics of fluids, gases and plasmas)
Birth date:
23.05.1959
E-mail: Website: https://www.mi.ras.ru/~ilichev Keywords: nonlinear waves,
dispersive and dissipative media,
hamiltonian systems,
orbital stability of bound states,
solitary waves,
exponential instability,
Evans' function,
collapse,
asymptotic methods,
qualitative theory of dynamical systems,
center manifold reduction,
normal forms.
Subject:
The scientific interests concern the propagation of nonlinear waves in dispersive and dissipative media, stability of localized wave structures and also of interfaces in fluid mechanics, elasticity, and filtration theory. A number of results were obtained about the existence and propagation of different types of solitary waves in dispersive and dissipative media of fluid mechanics. The results are included in the monography "Solitary waves in fluid dynamics". The problems are solved about the stability and instability of solitons in fluids, plasmas, elastic rods and composites and also of waveguide structures in the fluid. In a number of papers with G. G. Tsypkin a topological approach is adapted to investigation of stability of water-vapor interfaces in some models of hydrothermal systems. It was shown that stability of the interface persists for values of permeability, characteristic for natural hydrothermal reservoirs.
Main publications:
Haragus-Courcelle M., Ilichev A. Three dimensional solitary waves in the presence of additional surface effects // Eur. J. Mech. B/Fluids, 1998, 17, 739–768.
Ilichev A. Stability of solitary waves in nonlinear composite media // Physica D, 2001, 150, 264–277.
