Zobrazeno 1 - 10
of 61
pro vyhledávání: '"Rumanov, Igor"'
We derive the Whitham modulation equations for the nonlinear Schr\"odinger equation in the plane (2d NLS) with small dispersion. The modulation equations are derived in terms of both physical and Riemann variables; the latter yields equations of hydr
Externí odkaz:
http://arxiv.org/abs/2109.09719
The semi-classical Korteweg-deVries equation for step-like data is considered with a small parameter in front of the highest derivative. Using perturbation analysis Whitham theory is constructed to higher order. This allows the order one phase and th
Externí odkaz:
http://arxiv.org/abs/2006.03924
Dispersive shock waves (DSWs) of the defocusing radial nonlinear Schr\"odinger (rNLS) equation in two spatial dimensions are studied. This equation arises naturally in Bose-Einstein condensates, water waves and nonlinear optics. A unified nonlinear W
Externí odkaz:
http://arxiv.org/abs/1807.06723
Publikováno v:
J. Phys. A: Math. Theor. 51, 215501 (2018)
Whitham modulation theory for certain two-dimensional evolution equations of Kadomtsev-Petviashvili (KP) type is presented. Three specific examples are considered in detail: the KP equation, the two-dimensional Benjamin-Ono (2DBO) equation and a modi
Externí odkaz:
http://arxiv.org/abs/1711.03686
The appearance of a fundamental long-time asymptotic regime in the two space one time dimensional hyperbolic nonlinear Schr\"odinger (HNLS) equation is discussed. Based on analytical and extensive numerical simulations an approximate self-similar sol
Externí odkaz:
http://arxiv.org/abs/1606.02782
Autor:
Rumanov, Igor
This is a review of recent developments in the theory of beta ensembles of random matrices and their relations with conformal filed theory (CFT). There are (almost) no new results here. This article can serve as a guide on appearances and studies of
Externí odkaz:
http://arxiv.org/abs/1408.3847
Autor:
Rumanov, Igor
Publikováno v:
Commun. Math. Phys. 342, 843-868 (2016)
In arXiv:1306.2117, we found explicit Lax pairs for the soft edge of beta ensembles with even integer values of $\beta$. Using this general result, the case $\beta=6$ is further considered here. This is the smallest even $\beta$, when the correspondi
Externí odkaz:
http://arxiv.org/abs/1408.3779
Autor:
Rumanov, Igor
Publikováno v:
J. Math. Phys. 56, 013508 (2015)
Beta-ensembles of random matrices are naturally considered as quantum integrable systems, in particular, due to their relation with conformal field theory, and more recently appeared connection with quantized Painlev\'e Hamiltonians. Here we demonstr
Externí odkaz:
http://arxiv.org/abs/1306.2117
Autor:
Rumanov, Igor
Starting from the diffusion equation at beta random matrix hard edge obtained by Ramirez and Rider (2008), we study the question of its relation with Lax pairs for Painleve III. The results are in many respects similar to the ones found for soft edge
Externí odkaz:
http://arxiv.org/abs/1212.5333
Autor:
Rumanov, Igor
Tracy-Widom (TW) equations for one-matrix unitary ensembles (UE) (equivalent to a particular case of Schlesinger equations for isomonodromic deformations) are rewritten in a general form which allows one to derive all the lowest order equations (PDE)
Externí odkaz:
http://arxiv.org/abs/1008.3560