Connection formulae for the radial Toda equations I

Autor:	Guest, Martin A., Its, Alexander R., Kosmakov, Maksim, Miyahara, Kenta, Odoi, Ryosuke
Rok vydání:	2023
Předmět:	Mathematical Physics Mathematics - Classical Analysis and ODEs Nonlinear Sciences - Exactly Solvable and Integrable Systems
Druh dokumentu:	Working Paper
Popis:	This paper is the first in a forthcoming series of works where the authors study the global asymptotic behavior of the radial solutions of the 2D periodic Toda equation of type $A_n$. The principal issue is the connection formulae between the asymptotic parameters describing the behavior of the general solution at zero and infinity. To reach this goal we are using a fusion of the PDE analysis and the Riemann-Hilbert nonlinear steepest descent method of Deift and Zhou which is applicable to 2D Toda in view of its Lax integrability. A principal technical challenge is the extension of the nonlinear steepest descent analysis to Riemann-Hilbert problems of matrix rank greater than $2$. In this paper, we meet this challenge for the case $n=2$ (the rank $3$ case) and it already captures the principal features of the general $n$ case. Comment: 68 pages, 16 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2309.16550 Zobrazit plný text záznamu View this record from Arxiv