268 citations · 1.7k across the 77 of their papers we have counts for
78 papers
Gradient nature of Laplacian growth
A. Zabrodin
For a class of growth processes of Laplacian type in the plane, we suggest an interpretation as a ``gradient descent'' in the space of smooth closed curves. More precisely, we show…
Elliptic solutions to matrix CKP equation
A. Zabrodin
A class of elliptic solutions to the matrix CKP equation is studied. Equations of motion for their poles and matrix coefficients at the poles are obtained. As in the scalar case, t…
Dispersionless modified DKP hierarchy as the Yang-Baxter equation
A. Zabrodin
We show that the dispersionless version of the modified DKP hierarchy originally defined as the limit of relations for the tau-function of the Hirota-Miwa type has an equivalent re…
Monodromy free linear equations and many-body systems
I. Krichever, A. Zabrodin
We further develop the approach to many-body systems based on finding conditions of existence of meromorphic solutions to certain linear partial differential and difference equatio…
Toda lattice with constraint of type B
I. Krichever, A. Zabrodin
We introduce a new integrable hierarchy of nonlinear differential-difference equations which is a subhierarchy of the 2D Toda lattice defined by imposing a constraint to the Lax op…
Dispersionless version of the constrained Toda hierarchy and symmetric radial Löwner equation
Takashi Takebe, Anton Zabrodin
We study the dispersionless version of the recently introduced constrained Toda hierarchy. Like the Toda lattice itself, it admits three equivalent formulations: the formulation in…