发表机构
Universidade Federal de Santa Catarina; Instituto de Física de São Carlos, Universidade de São Paulo; Institute of Theoretical Physics, Jagiellonian University（圣卡塔琳娜联邦大学; 圣卡洛斯物理研究所，圣保罗大学; 雅盖隆大学理论物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文采用傅里叶方法推导符号-戈登模型的精确紧致振荡子，发现基频模式即可高精度近似，推广至摆动振荡子时需偶次模式，规避了相关不存在定理，为振荡子研究提供新框架。
AI 中文摘要
我们采用傅里叶方法，对符号-戈登（signum-Gordon）模型中的精确紧致振荡子进行了新的推导。该方法将振荡子分解为离散模式的无穷级数，这些模式由基频及其奇次高次谐波构成，且级数一致收敛，这与标准解析势的情况形成对比——在标准解析势中，对应的无穷微扰级数无法收敛。关键在于，我们的振荡子规避了空间局域化、小振幅周期态的不存在定理。我们研究了截断傅里叶级数的精度，发现仅基频模式就能为精确解提供极为准确的近似，当包含前两个非零谐波模式时，吻合度会显著提升。此外，我们将该框架推广到具有周期性运动边界的摆动紧致振荡子，表明描述此类振荡子需要偶次模式，这些模式与奇次源项的耦合会引发动态调制，进而产生摆动运动，即便空间傅里叶剖面本身是时间无关的。
英文摘要
We present a new derivation of the exact compact oscillon in the signum-Gordon model using Fourier methods. This approach decomposes the oscillon into an infinite, uniformly convergent series of discrete modes consisting of a fundamental frequency and its odd higher harmonics, in contrast to standard analytic potentials, where the corresponding infinite perturbative series fails to converge. Crucially, our oscillon evades the non-existence theorem for spatially localized, small-amplitude periodic states. We investigate the accuracy of truncating the Fourier series and find that the primary mode alone provides a remarkably accurate approximation of the exact solution, with agreement improving significantly when the first two non-vanishing harmonic modes are included. Furthermore, we generalize this framework to a swaying compact oscillon with a periodically moving boundary. We show that describing such an oscillon requires even-order modes, whose coupling with the odd source terms induces a dynamic modulation that generates the swaying motion, even though the spatial Fourier profiles themselves are time-independent.
Comments36 pages, 10 figures
