Alexander R. Its

collaborators

3 papers

math.AP2025

Nonlinear steepest descent on a torus: A case study of the Landau-Lifshitz equation

Harini Desiraju, Alexander R. Its, Andrei Prokhorov

We obtain rigorous large time asymptotics for the Landau-Lifshitz equation in the soliton free case by extending the nonlinear steepest descent method to genus 1 surfaces. The meth…

math-ph2025

Connection formulae for the radial Toda equations II

Martin A. Guest, Alexander R. Its, Maksim Kosmakov +2

This is a continuation of [arXiv:2309.16550] in which we computed the asymptotics near $x = \infty$ of all solutions of the radial Toda equation. In this article, we compute the as…

nlin.SI2024

The non-linear steepest descent approach to the singular asymptotics of the sinh-Gordon reduction of the PainlevÃ© III equation

Alexander R. Its, Kenta Miyahara, Maxim L. Yattselev

Motivated by the simplest case of tt*-Toda equations, we study the large and small $x$ asymptotics for $x > 0$ of real solutions of the sinh-Godron PainlevÃ© III( $D_{6}$ ) equation. The…