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Search Results: 1 - 10 of 563642 matches for " A. E. Mironov "
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On a Commutative Ring of Two Variable Differential Operators with Matrix Coefficients
A. E. Mironov
Physics , 2008,
Abstract: In this work, we construct commutative rings of two variable matrix differential operators that are isomorphic to a ring of meromorphic functions on a rational manifold obtained from the $CP^1\times CP^1$ by identification of two lines with the pole on a certain rational curve.
Discrete analogues of the Dixmier operators
A. E. Mironov
Physics , 2006, DOI: 10.1070/SM2007v198n10ABEH003890
Abstract: We construct discrete analogues of the Dixmier operators, that is, commuting difference operators corresponding to a spectral curve of genus 1 whose coefficients are polynomials of the discrete variable.
On Hamiltonian-Minimal Lagrangian Tori in CP^2
A. E. Mironov
Mathematics , 2006,
Abstract: We obtain some equations for Hamiltonian-minimal Lagrangian surfaces in CP^2 and give their particular solutions in the case of tori.
Spectral data for Hamiltonian-minimal Lagrangian tori in $CP^2$
A. E. Mironov
Mathematics , 2008,
Abstract: In this work, we find spectral data that allow to find Hamiltonian-minimal Lagrangian tori in $CP^2$ in terms of theta functions of spectral curves.
Real Commuting Differential Operators Connected with Two-Dimensional Abelian Varieties
A. E. Mironov
Mathematics , 2002,
Abstract: We indicate smooth real commuting matrix differential operators whose eigenvalues and eigenfunctions are parametrized by two-dimensional principally polarized abelian varieties.
Commutative rings of differential operators connected with two-dimensional Abelian varieties
A. E. Mironov
Mathematics , 2001,
Abstract: In this paper we find the explicit formulas of two dimensional commuting ($2\times 2$)-matrix differential operators which were introduced by Nakayashiki. The common eigen functions and eigen values of these operators are parametrized by the points of principally polarized Abelian varieties.
On nonlinear equations integrable in theta functions of nonprincipally polarized Abelian varieties
A. E. Mironov
Mathematics , 2001,
Abstract: The formula of expanding the Abel variety theta function restricted to Abel subvariety into theta functions of this subvariety is obtained. With the help of this formula the solution of differential equations with Jacobi theta functions, restricted on a nonprincipally polarized Abel subvariety and their translations are rewritten in terms of the theta functions of these subvarieties. This is exemplified by the CKP equations, the Bogoyavlenskij system, and the Toda $g_2^{(1)}$-chain.
Commutative Rings of Differential Operators Corresponding to Multidimensional Algebraic Varieties
A. E. Mironov
Mathematics , 2002,
Abstract: We construct new examples of multidimensional commuting matrix differential operators and a multidimensional analog of the Kadomtsev--Petviashvili hierarchy.
On new examples of Hamiltonian-minimal and minimal Lagrangian submanifolds in $C^n$ and $CP^n$
A. E. Mironov
Mathematics , 2003, DOI: 10.1070/SM2004v195n01ABEH000794
Abstract: We propose a new method for the construction of Hamiltonian-minimal and minimal Lagrangian immersions of some manifolds in $C^n$ and in $CP^n$. By this method one can construct, in particular, immersions of such manifolds as the generalized Klein's bottle $K^n$, the multidimensional torus, $K^{n-1}\times S^1$, $S^{n-1}\times S^1$, and others. In some cases these immersions are embeddings. For example, it is possible to embed the following manifolds: $K^{2n+1},$ $S^{2n+1}\times S^1$, $K^{2n+1}\times S^1$, $S^{2n+1}\times S^1\times S^1$.
The Novikov-Veselov hierarchy of equations and integrable deformations of minimal Lagrangian tori in CP^2
A. E. Mironov
Mathematics , 2006,
Abstract: We associate a periodic two-dimensional Schrodinger operator to every Lagrangian torus in CP^2 and define the spectral curve of a torus as the Floquet spectrum of this operator on the zero energy level. In this event minimal Lagrangian tori correspond to potential operators. We show that Novikov-Veselov hierarchy of equations induces integrable deformations of minimal Lagrangian torus in CP^2 preserving the spectral curve. We also show that the highest flows on the space of smooth periodic solutions of the Tzizeica equation are given by the Novikov-Veselov hierarchy.
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