新耦合可积无色散方程的规范变换和长渐近性

IF 0.9 3区数学 Q3 MATHEMATICS, APPLIED

Mathematical Physics, Analysis and Geometry Pub Date : 2025-05-02 DOI:10.1007/s11040-025-09507-1

Xumeng Zhou, Xianguo Geng, Minxin Jia, Yunyun Zhai

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引用次数: 0

摘要

本文研究了一类新的耦合可积无色散方程Cauchy问题解的渐近行为分析。利用规范变换、谱分析和逆散射方法，我们证明了新的耦合可积无色散方程的解可以用复数\(\lambda \) -平面上的两个矩阵Riemann-Hilbert问题的解来表示。将非线性最陡下降法应用于两个相关的矩阵值Riemann-Hilbert问题，得到了新的耦合可积无色散方程解的精确的前阶渐近公式和一致的误差估计。

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Gauge Transformations and Long-Time Asymptotics for the New Coupled Integrable Dispersionless Equations

This work aims to investigate the asymptotic behavior analysis of solutions to the Cauchy problem of new coupled integrable dispersionless equations. Utilizing the gauge transformations, spectral analysis and inverse scattering method, we show that the solutions of new coupled integrable dispersionless equations can be expressed in terms of the solutions of two matrix Riemann–Hilbert problems formulated in the complex \(\lambda \)-plane. Applying the nonlinear steepest descent method to the two associated matrix-valued Riemann–Hilbert problems, we obtain precise leading-order asymptotic formulas and uniform error estimates for the solutions of new coupled integrable dispersionless equations.

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来源期刊

Mathematical Physics, Analysis and Geometry 数学-物理：数学物理

CiteScore

2.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： MPAG is a peer-reviewed journal organized in sections. Each section is editorially independent and provides a high forum for research articles in the respective areas. The entire editorial board commits itself to combine the requirements of an accurate and fast refereeing process. The section on Probability and Statistical Physics focuses on probabilistic models and spatial stochastic processes arising in statistical physics. Examples include: interacting particle systems, non-equilibrium statistical mechanics, integrable probability, random graphs and percolation, critical phenomena and conformal theories. Applications of probability theory and statistical physics to other areas of mathematics, such as analysis (stochastic pde''s), random geometry, combinatorial aspects are also addressed. The section on Quantum Theory publishes research papers on developments in geometry, probability and analysis that are relevant to quantum theory. Topics that are covered in this section include: classical and algebraic quantum field theories, deformation and geometric quantisation, index theory, Lie algebras and Hopf algebras, non-commutative geometry, spectral theory for quantum systems, disordered quantum systems (Anderson localization, quantum diffusion), many-body quantum physics with applications to condensed matter theory, partial differential equations emerging from quantum theory, quantum lattice systems, topological phases of matter, equilibrium and non-equilibrium quantum statistical mechanics, multiscale analysis, rigorous renormalisation group.