poincar - lindstedt级数解译的时间周期解的复杂结构：S3上的三次共形波动方程

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena Pub Date : 2025-08-08 DOI:10.1016/j.physd.2025.134864

Filip Ficek , Maciej Maliborski

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引用次数: 0

摘要

本文探讨了S3上三次共形波动方程球对称时周期解的丰富结构。我们发现从线性化方程的特征模态分叉的解族形成了类似于三次波动方程所观察到的模式。除了Galerkin方法外，我们还使用基于pad近似的新方法来研究它们。为此，我们提供了解的严格摄动构造。由于共形对称性，本文给出的解可以作为反德西特背景下共形耦合标量场大时间周期解的例子。

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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Complex structure of time-periodic solutions decoded in Poincaré–Lindstedt series: The cubic conformal wave equation on S3

This work explores the rich structure of spherically symmetric time-periodic solutions of the cubic conformal wave equation on

S^{3}

. We discover that the families of solutions bifurcating from the eigenmodes of the linearized equation form patterns similar to the ones observed for the cubic wave equation. Alongside the Galerkin approaches, we study them using the new method based on the Padé approximants. To do so, we provide a rigorous perturbative construction of solutions. Due to the conformal symmetry, the solutions presented in this work serve as examples of large time-periodic solutions of the conformally coupled scalar field on the anti-de Sitter background.

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来源期刊

Physica D: Nonlinear Phenomena 物理-物理：数学物理

CiteScore

7.30

自引率

7.50%

发文量

213

审稿时长

65 days

期刊介绍： Physica D (Nonlinear Phenomena) publishes research and review articles reporting on experimental and theoretical works, techniques and ideas that advance the understanding of nonlinear phenomena. Topics encompass wave motion in physical, chemical and biological systems; physical or biological phenomena governed by nonlinear field equations, including hydrodynamics and turbulence; pattern formation and cooperative phenomena; instability, bifurcations, chaos, and space-time disorder; integrable/Hamiltonian systems; asymptotic analysis and, more generally, mathematical methods for nonlinear systems.