发表机构
School of Mathematics and Statistics, Henan University; School of Mathematics and Statistics, North China University of Water Resources and Electric Power; School of Mathematics and Statistics, Zhengzhou University（河南大学数学与统计学院; 华北水利水电大学数学与统计学院; 郑州大学数学与统计学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过规范变换、谱分析和逆散射方法，将海森堡铁磁方程的解转化为矩阵Riemann-Hilbert问题，并利用非线性最速下降法得到了解的精确首阶渐近公式和一致误差估计。
AI 中文摘要
本文旨在研究具有Schwartz初值的海森堡铁磁方程柯西问题解的长时间渐近行为。利用规范变换、谱分析和逆散射方法，我们证明了海森堡铁磁方程的解可以用复$k$-平面中构造的矩阵Riemann-Hilbert问题的解来表示。给出了各种Deift-Zhou轮廓变形及其背后的动机。通过将非线性最速下降法应用于相关的矩阵值Riemann-Hilbert问题，我们获得了海森堡铁磁方程柯西问题解的精确首阶渐近公式和一致误差估计。
英文摘要
This work aims to investigate the long-time asymptotic behavior of solutions to the Cauchy problem for the Heisenberg ferromagnet equation with the Schwartz initial data. Utilizing the gauge transformations, spectral analysis and the inverse scattering method, we prove that the solutions to the Heisenberg ferromagnet equation can be expressed in terms of the solutions to a matrix Riemann-Hilbert problem formulated in the complex $k$-plane. Various Deift-Zhou contour deformations and the motivation behind them are given. By applying the nonlinear steepest descent method to the associated matrix-valued Riemann-Hilbert problem, we obtain the exact leading-order asymptotic formulas and uniform error estimates for solutions to the Cauchy problem of the Heisenberg ferromagnet equation.
