## On Universality of Critical Behavior in the Focusing Nonlinear Schrödinger Equation, Elliptic Umbilic Catastrophe and the Tritronquée Solution to the Painlevé-I Equation

- B. Dubrovin, T. Grava, C. Klein
- MathematicsJournal of nonlinear science
- 1 February 2009

## A representation of joint moments of CUE characteristic polynomials in terms of Painlevé functions

- E. Basor, P. Bleher,
+4 authors J. Keating - MathematicsNonlinearity
- 31 October 2018

We establish a representation of the joint moments of the characteristic polynomial of a CUE random matrix and its derivative in terms of a solution of the -Painlevé V equation. The derivation… Expand

## Rigorous Asymptotics of a KdV Soliton Gas

- M. Girotti, T. Grava, R. Jenkins, K. Mclaughlin
- MathematicsCommunications in Mathematical Physics
- 2 July 2018

We analytically study the long time and large space asymptotics of a new broad class of solutions of the KdV equation introduced by Dyachenko, Zakharov, and Zakharov. These solutions are… Expand

## Numerical solution of the small dispersion limit of Korteweg—de Vries and Whitham equations

The Cauchy problem for the Korteweg—de Vries (KdV) equation with small dispersion of order ϵ2, ϵ ≪ 1, is characterized by the appearance of a zone of rapid, modulated oscillations of wavelength of… Expand

## Solitonic Asymptotics for the Korteweg-de Vries Equation in the Small Dispersion Limit

## Universality of the Break-up Profile for the KdV Equation in the Small Dispersion Limit Using the Riemann-Hilbert Approach

AbstractWe obtain an asymptotic expansion for the solution of the Cauchy problem for the Korteweg-de Vries (KdV) equation
$$u_t+6uu_x+\epsilon^{2}u_{xxx}=0,\quad u(x,t=0,\epsilon)=u_0(x),$$for… Expand

## The generation, propagation, and extinction of multiphases in the KdV zero‐dispersion limit

We study the multiphases in the KdV zero‐dispersion limit. These phases are governed by the Whitham equations, which are 2g + 1 quasi‐linear hyperbolic equations where g is the number of phases. We… Expand

## Thomae Type Formulae For Singular ZN Curves

- V. Enolski, T. Grava
- Mathematics
- 7 February 2006

AbstractWe give an elementary and rigorous proof of the Thomae type formula for the singular curves
$$\mu^N=\prod_{j=1}^m(\lambda-\lambda_{2j})^{N-1}\prod_{j=0}^{m}(\lambda-\lambda_{2j+1})$$. To… Expand

## Laguerre Ensemble: Correlators, Hurwitz Numbers and Hodge Integrals

- Massimo Gisonni, T. Grava, G. Ruzza
- MathematicsAnnales de l'Institute Henri Poincare. Physique…
- 2 December 2019

We consider the Laguerre partition function and derive explicit generating functions for connected correlators with arbitrary integer powers of traces in terms of products of Hahn polynomials. It was… Expand

## Orthogonal Polynomials for a Class of Measures with Discrete Rotational Symmetries in the Complex Plane

We obtain the strong asymptotics of polynomials $$p_n(\lambda )$$pn(λ), $$\lambda \in {\mathbb {C}}$$λ∈C, orthogonal with respect to measures in the complex plane of the form $$\begin{aligned} \hbox… Expand

...

1

2

3

4

5

...