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The stability of non-linear Integrable Optics Test Accelerator (IOTA) model was tested. The area of the stable region in transverse coordinates and the maximum attainable tune spread were found as a f...
Integrable equations and classical S-matrix     Integrable equations  classical S-matrix  Mathematical Physics       font style='font-size:12px;'> 2012/4/26
We study amplitudes of five-wave interactions for evolution Hamiltonian equations differ from the KdV equation by the form of dispersion law. We find that five-wave amplitude is canceled for all three...
The main purpose of this paper is to introduce a new class of Hamiltonian scattering systems of the cone potential type that can be integrated via the asymptotic velocity. For a large subclass, the as...
We give integrable quad equations which are multi-quadratic (degree-two) counterparts of the well-known multi-affine (degree-one) equations classified by Adler, Bobenko and Suris (ABS). These multi-qu...
We construct a family of integrable Hamiltonian systems parametrized by pairs of Coxeter elements in the affine Weyl group. Their phase spaces are double Bruhat cells in the corresponding Kac-Moody gr...
Ring for test of nonlinear integrable optics     Ring  test  nonlinear integrable optics  Nonlinear optics       font style='font-size:12px;'> 2012/2/28
Nonlinear optics is a promising idea potentially opening the path towards achieving super high beam intensities in circular accelerators. Creation of a tune spread reaching 50% of the betatron tune wo...
Dimers and cluster integrable systems     cluster integrable systems  Algebraic Geometry       font style='font-size:12px;'> 2011/9/22
Abstract: We show that the dimer model on a bipartite graph on a torus gives rise to a quantum integrable system of special type - a cluster integrable system. The phase space of the classical system ...
Abstract: Two planar supersymmetric quantum mechanical systems built around the quantum integrable Kepler/Coulomb and Euler/Coulomb problems are analyzed in depth. The supersymmetric spectra of both s...
Abstract: We study the Hamiltonian vector field $v=(-\partial f/\partial w,\partial f/\partial z)$ on $\mathbb C^2$, where $f=f(z,w)$ is a polynomial in two complex variables, which is non-degenerate ...
Dimer Models and Integrable Systems     Dimer Models  Integrable Systems  High Energy Physics - Theory       font style='font-size:12px;'> 2011/9/29
Abstract: We explore various aspects of the correspondence between dimer models and integrable systems recently introduced by Goncharov and Kenyon. Dimer models give rise to relativistic integrable sy...
Abstract: We consider integrable discretizations of some soliton equations associated with the motions of plane curves: the Wadati-Konno-Ichikawa elastic beam equation, the complex Dym equation, and t...
This is a proceedings article reviewing a recent combinatorial construction of the su(n) WZNW fusion ring by C. Stroppel and the author. It contains one novel aspect: the explicit derivation of an alg...
Abstract: This is a proceedings article reviewing a recent combinatorial construction of the su(n) WZNW fusion ring by C. Stroppel and the author. It contains one novel aspect: the explicit derivation...
The purpose of this article is to show that a $\mathcal{C}^1$ differential system on $\R^n$ which admits a set of $n-1$ independent $\mathcal{C}^2$ conservation laws defined on an open subset $\Omega\...
W-extended Kac representations and integrable boundary conditions in the logarithmic minimal models WLM(1,p).

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