32 citations · 93 across the 12 of their papers we have counts for
14 papers
On the Whitham system for the (2+1)-dimensional nonlinear Schrödinger equation
Mark J. Ablowitz, Justin T. Cole, Igor Rumanov
We derive the Whitham modulation equations for the nonlinear Schrödinger equation in the plane (2d NLS) with small dispersion. The modulation equations are derived in terms of both…
Whitham equations and phase shifts for the Korteweg-deVries equation
Mark J. Ablowitz, Justin T. Cole, Igor Rumanov
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…
On the Whitham system for the radial nonlinear Schrödinger equation
Mark J. Ablowitz, Justin T. Cole, Igor Rumanov
Dispersive shock waves (DSWs) of the defocusing radial nonlinear Schrödinger (rNLS) equation in two spatial dimensions are studied. This equation arises naturally in Bose-Einstein…
Whitham modulation theory for (2+1)-dimensional equations of Kadomtsev-Petviashvili type
Mark J. Ablowitz, Gino Biondini, Igor Rumanov
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…
A universal asymptotic regime in the hyperbolic nonlinear Schrödinger equation
Mark J. Ablowitz, Yi-Ping Ma, Igor Rumanov
The appearance of a fundamental long-time asymptotic regime in the two space one time dimensional hyperbolic nonlinear Schrödinger (HNLS) equation is discussed. Based on analytical…
Beta ensembles, quantum Painlevé equations and isomonodromy systems
Igor Rumanov
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…
Painlevé representation of Tracy-Widom distribution for
Igor Rumanov
In arXiv:1306.2117, we found explicit Lax pairs for the soft edge of beta ensembles with even integer values of . Using this general result, the case is further considered…
Classical integrability for beta-ensembles and general Fokker-Planck equations
Igor Rumanov
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 appear…
Hard edge for beta-ensembles and Painlevé III
Igor Rumanov
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. Th…
All the lowest order PDE for spectral gaps of Gaussian matrices
Igor Rumanov
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 genera…
Various equations for gap probabilities of coupled Gaussian matrices
Igor Rumanov
Versions of Tracy-Widom (TW) and Adler-Shiota-van Moerbeke (ASvM) approaches are applied to derive various partial differential equations (PDE) satisfied by joint eigenvalue spacin…
Universal Structure and Universal PDE for Unitary Ensembles
Igor Rumanov
An attempt is made to describe random matrix ensembles with unitary invariance of measure (UE) in a unified way, using a combination of Tracy-Widom (TW) and Adler-Shiota-Van Moerbe…
The correspondence between Tracy-Widom (TW) and Adler-Shiota-van Moerbeke (ASvM) approaches in random matrix theory: the Gaussian case
Igor Rumanov
Two approaches (TW and ASvM) to derivation of integrable differential equations for random matrix probabilities are compared. Both methods are rewritten in such a form that simple…
About Entropy Dependence on Observer
Igor Rumanov
It is shown that the entropy of systems with large number of degrees of freedom is practically independent of observers, contrary to the claim of hep-th/0310022.