Long-time asymptotic behavior for the defocusing Hirota equation on a finite-genus algebro-geometric background

2026/07/21 by Taohua Luo, Zhenya Yan, Guoqiang Zhang · 1 voice
#nlin.SI #math-ph #math.AP #math.MP #nlin.PS #physics.optics

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Abstract

In this paper, we investigate the long-time asymptotics for the solution of the Cauchy problem of the defocusing Hirota equation on a finite-genus algebro-geometric background in the whole (x,t)-half-plane, whose method is mainly based on a Riemann-Hilbert (RH) formulation and Deift-Zhou nonlinear steepest descent method. The critical values of the phase function in the associated RH problem divide the space-time plane into four regions, in which the leading-order term is given by a phase-shifted finite-genus algebro-geometric solution. The subleading behavior depends on the region: the correction is of order t^-1/3 and is governed by a Painlevé-XXXIV model RH problem in the transition regions; the leading radiation is of order t^-1/2 in the Zakharov--Manakov region; and the error is O(t^-1) in the fast-decay region. These results can also be extended to other higher-order members of the AKNS hierarchy.

Citations

• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems

Discussions

• Taohua Luo, Zhenya Yan, Guoqiang Zhang: Long-time asymptotic behavior for the defocusing Hirota equation on a finite-genus algebro-geometric background https://arxiv.org/abs/2607.19119 https://arxiv.o [bsky, 0 points, 0 comments]

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