14 citations · 34 across the 6 of their papers we have counts for
6 papers
Algebraic non-integrability of magnetic billiards on the Sphere and Hyperbolic plane
Misha Bialy, Andrey E. Mironov
We consider billiard ball motion in a convex domain on a constant curvature surface influenced by the constant magnetic field. We examine the existence of integral of motion which…
On the Nonrelativistic 2D Purely Magnetic Supersymmetric Pauli Operator
P. Grinevich, A. Mironov, S. Novikov
The Complete Manifold of Ground State Eigenfunctions for the Purely Magnetic 2D Pauli Operator is considered as a by-product of the new reduction found by the present authors few y…
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…
New Reductions and Nonlinear Systems for 2D Schrodinger Operators
P. Grinevich, A. Mironov, S. Novikov
New Completely Integrable (2+1)-System is studied. It is based on the so-called L-A-B-triples where L is a 2D Schrodinger Operator. This approach was invented by S.M…
Orthogonal curvilinear coordinate systems corresponding to singular spectral curves
A. E. Mironov, I. A. Taimanov
We study the limiting case of the Krichever construction of orthogonal curvilinear coordinate systems when the spectral curve becomes singular. We show that the case when the curve…