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

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arxiv 2405.17662 v4 pith:B2OQ4AVB submitted 2024-05-27 math.AP math-phmath.MPnlin.SI

Harini Desiraju , Alexander R. Its , Andrei Prokhorov This is my paper · ORCID
classification math.APmath-phmath.MPnlin.SI
keywords equationlandau-lifshitzanalysiscasedescentnonlinearrigoroussteepest
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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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  1. Matrix valued orthogonal polynomials arising from hexagon tilings with 3x3-periodic weightings

    math.CA 2024-12 conditional novelty 7.0 of 10

    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 spectr...

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