相关论文: Generalized Lame operators
We introduce two integral representations of monodromy on Lam\'e equation. By applying them, we obtain results on hyperelliptic-to-elliptic reduction integral formulae, finite-gap potential and eigenvalues of Lam\'e operator.
In this paper, we investigate new integrable extensions of two-center Coulomb systems. We study the most general $n$-dimensional deformation of the two-center problem by adding arbitrary functions supporting second order commuting conserved…
We give an analytical description of the locus of the two-gap elliptic potentials associated with the corresponding flow of the Calogero--Moser system. We start with the description of Treibich--Verdier two--gap elliptic potentials. The…
We shall generalize the notion of a Laver table to algebras which may have many generators, several fundamental operations, fundamental operations of arity higher than 2, and to algebras where only some of the operations are…
We investigate the relation between the symmetries of a Schr\"odinger operator and the related topological quantum numbers. We show that, under suitable assumptions on the symmetry algebra, a generalization of the Bloch-Floquet transform…
It is well known that the matrix of a metaplectic operator with respect to phase-space shifts is concentrated along the graph of a linear symplectic map. We show that the algebra generated by metaplectic operators and by pseudodifferential…
In this paper, we aim to present new extensions of incomplete gamma, beta, Gauss hypergeometric, confluent hypergeometric function and Appell-Lauricella hypergeometric functions, by using the extended Bessel function due to Boudjelkha [4].…
Using a new definition of generalized divisors we prove that the lattice of such divisors for a given linear partial differential operator is modular and obtain analogues of the well-known theorems of the Loewy-Ore theory of factorization…
In this paper, we study Schr\"{o}dinger equations on elliptic curves called generalized Lam\'{e} equations. We suggest a method of finding integrable potentials for Schr\"{o}dinger type equations. We apply this method to the Lam\'{e}…
The equivalence between the N-particle Calogero-Moser systems and the integrable sl(N,$\mathbb{C}$)-tops is shown. New rational and trigonometric classical Lax operators for these systems are found. Relations with new solutions of the…
For linear operators which factor with suitable assumptions concerning commutativity of the factors, we introduce several notions of a decomposition. When any of these hold then questions of null space and range are subordinated to the same…
In this paper, we consider $L^p$- estimate for a class of oscillatory integral operators satisfying the Carleson-Sj\"olin conditions with further convex and straight assumptions. As applications, the multiplier problem related to a general…
The aim of this paper is to summarize some recently obtained relations between the Ablowitz-Ladik hierarchy (ALH) and other integrable equations. It has been shown that solutions of finite subsystems of the ALH can be used to derive a wide…
We show that elliptic Calogero-Moser system and its Lax operator found by Krichever can be obtained by Hamiltonian reduction from the integrable Hamiltonian system on the cotangent bundle to the central extension of the algebra of SL(N,C)…
We outline an approach to a theory of various generalizations of the elliptic Calogero-Moser (CM) and Ruijsenaars-Shneider (RS) systems based on a special inverse problem for linear operators with elliptic coefficients. Hamiltonian theory…
In this article, we investigate systems of generalized Schr\"odinger operators and their fundamental matrices. More specifically, we establish the existence of such fundamental matrices and then prove sharp upper and lower exponential decay…
Integrable discretisations for a class of coupled (super) nonlinear Schrodinger (NLS) type of equations are presented. The class corresponds to a Lax operator with entries in a Grassmann algebra. Elementary Darboux transformations are…
In this note, we obtain sharp bounds for the Green's function of the linearized Monge-Amp\`ere operators associated to convex functions with either Hessian determinant bounded away from zero and infinity or Monge-Amp\`ere measure satisfying…
We present some general theorems about operator algebras that are algebras of functions on sets, including theories of local algebras, residually finite dimensional operator algebras and algebras that can be represented as the scalar…
Our paper investigates one-dimensional Schr\"odinger operators defined as closed operators on $L^2(\mathbb{R})$ or $L^2(\mathbb{R}_+)$ that are exactly solvable in terms of confluent functions (or, equivalently, Whittaker functions). We…