Work

Connection formulae for the radial Toda equations I

Year: 2025

Type: article

Abstract: 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 An . 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 Iwasawa factorization in the loop group theory 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.

Source: Nonlinearity

DOI: 10.1088/1361-6544/adb238

Authors: Martin A Guest, Alexander R Its, Maksim Kosmakov, Kenta Miyahara, Ryosuke Odoi

Institutions: Waseda University, Indiana University Indianapolis, University of Cincinnati

Language: English

Topic: Nonlinear Waves and Solitons

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funders: Royal Society, Russian Science Foundation, Japan Society for the Promotion of Science, Division of Mathematical Sciences

Awards: Homotopy theory related to toric varieties and its related geomety, The tt* equations: a bridge between the differential geometry of moduli spaces and classical isomonodromy theory, G7185436590, G7614273139, Differential geometry and integrable systems: exploiting new links