We establish a duality between the quantum wave vector spectrum and the eigenmodes of the classical Liouvillian dynamics for integrable billiards. Signatures of the classical eigenmodes appear as peaks in the correlation function of the quantum wave vector spectrum. A semiclassical derivation and numerical calculations are presented in support of the results. These classical eigenmodes can be o...

Abstract We propose a systematic method to generalize the integrable Rosochatius deformations for finite dimensional integrable Hamiltonian systems to integrable Rosochatius deformations for infinite dimensional integrable equations. Infinite number of the integrable Rosochatius deformed higher-order constrained flows of some soliton hierarchies, which includes the generalized integrable Hénon-...

Integrable dispersionless Kadomtsev-Petviashvili (KP) hierarchy of B type is considered. Addition formula for the τ -function and conformally invariant equations for the dispersionless BKP (dBKP) hierarchy are derived. Symmetry constraints for the dBKP hierarchy are studied.

A locally integrable function m(ξ, η) defined on R × R is said to be a bilinear multiplier on R of type (p1, p2, p3) if Bm(f, g)(x) = Z

A new type of an integrable mapping is presented. This map is equipped with fractional difference and possesses an exact solution, which can be regarded as a discrete analogue of the Mittag-Leffler function.

Suppose that Ω is an integrable function on S. We study the singular integral operator TΩf = p.v. f ∗ Ω(x/|x|) |x|2 . We show that for α > 0 the condition

Conditions for a function (number sequence) to be a multiplier on the space of integrable functions on R (T) are given. This generalizes recent results of Giang and Moricz.

In this paper we present a family of second order in time nonlinear partial differential equations, which have only one higher symmetry. These equations are not integrable, but have a solution depending on one arbitrary function.

In this paper there are many important results of q-Fourier analysis proved by new ways and new sets of markov operators acting on the Lq,2,v space of square q-integrable function which were defined.

We consider the long time limit theorems for the solutions of a discrete wave equation with a weak stochastic forcing. The multiplicative noise conserves the energy, and in the unpinned case also conserves the momentum. We obtain a time-inhomogeneous OrnsteinUhlenbeck equation for the limit wave function that holds both for square integrable and statistically homogeneous initial data. The limit...