For a symmetric subclass of 3x3-periodic hexagon tilings, the associated matrix valued orthogonal polynomials admit a full asymptotic expansion built from an explicit balayage equilibrium measure on a genus one spectral curve.
Nonlinear steepest descent on a torus: A case study of the Landau-Lifshitz equation
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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 methods presented in this paper pave the way to a rigorous analysis of other integrable equations on the torus and enable asymptotic analysis on different regimes of the Landau-Lifshitz equation.
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Matrix valued orthogonal polynomials arising from hexagon tilings with 3x3-periodic weightings
For a symmetric subclass of 3x3-periodic hexagon tilings, the associated matrix valued orthogonal polynomials admit a full asymptotic expansion built from an explicit balayage equilibrium measure on a genus one spectral curve.