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Creators/Authors contains: "Odoi, Ryosuke"

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  1. ; ; ; ; (, Nonlinearity)
    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 typeAn. 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 casen = 2 (the rank 3 case) and it already captures the principal features of the generalncase. 
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    Free, publicly-accessible full text available February 18, 2026