Research Interests

• Combustion waves: Instabilities in combustion, combustion waves and pattern formation in premixed and diffusion flames.
• Nonlinear waves: Stability, dynamics and interaction of the solitary waves and fronts; Evans function method, exterior algebra and its applications to the linear stability of traveling waves; combustion waves, waves in chemical reactions, solitons in Bose-Einstein condensate.
• Chaotic dynamics: Chaos in radiophysics, chaotic dynamics of nonlinear waves.
• Atomic physics: Atomic optics, atom cooling and trapping, interactions of atoms in external field, Bose-Einstein condensate.
• Biophysics: Turing and non-Turing mechanisms of pattern formation; modeling of self-organization in biological and chemical systems; tumor growth.
• Numerical methods: Stiff differential equations, compound matrix method, geometrical integrators, PDEs.