Igor Loutsenko

Learn More
A new class of linear second order hyperbolic partial differential operators satisfying Huygens’ principle in Minkowski spaces is presented. The construction reveals a direct connection between Huygens’ principle and the theory of solitary wave solutions of the Korteweg-de Vries equation. Mathematics Subject Classification: 35Q51, 35Q53, 35L05, 35L15, 35Q05.
The theory of quadrature domains for harmonic functions and the Hele-Shaw problem of the fluid dynamics are related subjects of the complex variables and mathematical physics. We present results generalizing the above subjects for elliptic PDEs with variable coefficients, emerging in a class of the free-boundary problems for viscous flows in non-homogeneous(More)
We discuss the possibility for a moving droplet of excitons and phonons to form a coherent state inside the packet. We describe such an inhomogeneous state in terms of Bose-Einstein condensation and prescribe it a macroscopic wave function. Existence and, thus, coherency of such a Bosecore inside the droplet can be checked experimentally by letting two(More)
The theory of quadrature domains for harmonic functions and the Hele-Shaw problem of the fluid dynamics are related subjects of the complex variables and mathematical physics. We present results generalizing the above subjects for elliptic PDEs with variable coefficients, emerging in a class of the free-boundary problems for viscous flows in non-homogeneous(More)