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7 papers · 1 filter
2D Schrodinger Operator, (2+1) Systems and New Reductions. The 2D Burgers Hierarchy and Inverse Problem Data
P. Grinevich, A. Mironov, S. Novikov
The Theory of (2+1) Systems based on 2D Schrodinger Operator was started by S.Manakov, B.Dubrovin, I.Krichever and S.Novikov in 1976. The Analog of Lax Pairs introduced by Manakov,…
On the Ground Level of Purely Magnetic Algebro-Geometric 2D Pauli Operator (spin 1/2)
P. Grinevich, A. Mironov, S. Novikov
Full manifold of the complex Bloch-Floquet eigenfunctions is investigated for the ground level of the purely magnetic 2D Pauli operators (equal to zero because of supersymmetry). D…
Two-dimensional rational solitons and their blow-up via the Moutard transformation
I. A. Taimanov, S. P. Tsarev
By using the Moutard transformation of two-dimensional Schroedinger operators we derive a procedure for constructing explicit examples of such operators with rational fast decaying…
On problem of polarization tomography, I
Roman Novikov, Vladimir Sharafutdinov
The polarization tomography problem consists of recovering a matrix function f from the fundamental matrix of the equation known for every geodesic of a giv…
On some algebraic examples of Frobenius manifolds
A. E. Mironov, I. A. Taimanov
We construct some explicit quasihomogeneous algebraic solutions to the associativity (WDVV) equations by using analytical methods of the finite gap integration theory. These soluti…
Commutative Rings of Differential Operators Corresponding to Multidimensional Algebraic Varieties
A. E. Mironov
We construct new examples of multidimensional commuting matrix differential operators and a multidimensional analog of the Kadomtsev--Petviashvili hierarchy.