16 citations · 64 across the 28 of their papers we have counts for
6 papers · 1 filter
Loewner evolution and finite dimensional reductions of integrable systems
Maxim V. Pavlov, Dmitri Prokhorov, Alexander Vasil'ev +1
The Loewner equation is known as a one-dimensional reduction of the Benney chain as well as the dispersionless KP hierarchy. We propose a reverse process showing that time splittin…
Evolution of smooth shapes and integrable systems
Irina Markina, Alexander Vasil'ev
We consider a homotopic evolution in the space of smooth shapes starting from the unit circle. Based on the Loewner-Kufarev equation we give a Hamiltonian formulation of this evolu…
Conformal field theory and Loewner-Kufarev evolution
Irina Markina, Alexander Vasil'ev
One of the important aspects in recent trends in complex analysis has been the increasing degree of cross-fertilization between the latter and mathematical physics with great benef…
Virasoro Algebra and Löwner-Kufarev Equations
Irina Markina, Alexander Vasil'ev
Contour dynamics is a classical subject both in physics and in complex analysis. We show that the dynamics provided by the Löwner-Kufarev ODE and PDE possesses a rigid algebraic st…
Energy characteristics of subordination chains
Alexander Vasil'ev
We consider subordination chains of simply connected domains with smooth boundaries in the complex plane. Such chains admit Hamiltonian and Lagrangian interpretations through the L…
Liouville and logarithmic actions in Laplacian growth
Alexander Vasil'ev
We discuss and construct an action functional (logarithmic action) for the simply connected Laplacian growth and obtain its variation. This variation admits various interpretations…