Spectral stability of elliptic function solutions for the short pulse equation

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations Pub Date : 2026-04-15 Epub Date: 2026-01-14 DOI:10.1016/j.jde.2026.114099

Li-Ming Cao, Shou-Fu Tian

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引用次数: 0

Abstract

The main purpose of this work is to investigate the spectral stability of elliptic function solutions for the short pulse equation, a completely integrable model for the description of ultra-short pulse propagation in optical fibers. Recently, Yang and Fan developed

\bar{\partial}

-steepest descent method to analyze the long-time asymptotic behavior for the short pulse equation (Yang and Fan (2021) [50]). Subsequently, Li, Tian and Yang extended their results and reported the asymptotic stability of N-soliton solution (Li et al. (2023) [33]). Inspired by these works, we consider the spectral stability for three classes of elliptic solutions which are derived via the algebraic geometry method in this work. It is worth noting that the Lax spectrum in focusing case is not restricted to imaginary axis. To address this issue, we develop the squared wavefunction method using Jacobi theta function theory, and then establish spectral stability for both focusing and defocusing cases.

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短脉冲方程椭圆函数解的谱稳定性

本文的主要目的是研究用于描述超短脉冲在光纤中传播的完全可积模型——短脉冲方程的椭圆函数解的谱稳定性。最近，Yang和Fan开发了∂¯-最陡下降方法来分析短脉冲方程的长时间渐近行为（Yang和Fan(2021)[50]）。随后，Li、Tian和Yang扩展了他们的结果，报道了n孤子解的渐近稳定性（Li et al.(2023)[33]）。受这些工作的启发，本文研究了用代数几何方法导出的三类椭圆解的谱稳定性。值得注意的是，聚焦情况下的Lax光谱并不局限于虚轴。为了解决这个问题，我们利用Jacobi theta函数理论开发了平方波函数方法，然后建立了聚焦和散焦情况下的光谱稳定性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Differential Equations 数学-数学

CiteScore

4.40

自引率

8.30%

发文量

543

审稿时长

9 months

期刊介绍： The Journal of Differential Equations is concerned with the theory and the application of differential equations. The articles published are addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools. Research Areas Include: • Mathematical control theory • Ordinary differential equations • Partial differential equations • Stochastic differential equations • Topological dynamics • Related topics