The laboratory studies problems in mechanics, physics, biology by analytical, asymptotic and numerical methods. The main areas of research can be identified:

• Study of nonlinear dynamic processes in media with complex internal structure and in metamaterials.
• Development of asymptotic methods for deriving nonlinear model wave equations in partial derivatives.
• Development of analytical and numerical methods for solving nonlinear wave equations in partial derivatives
• Development of methods for controlling nonlinear waves in media with a complex internal structure and in metamaterials.
• Development of a nonlinear model of deformation of crystalline bodies with a complex lattice.
• Investigation by molecular dynamics methods of structures and defects in nanoscopic nematic films, as well as equilibrium structures and flow of various liquids in nanochannels.
• Investigation of the behavior of active nematics in closed two-dimensional nanoscopic regions within the framework of the nanoscopic model of active self-propelled particles.

Fig. Nanoscopic model of active self-propelled particles.

• Study of the effect of hydrogen accumulation and extraction on the properties of metals.