Chirilus-Bruckner Martina, Cuevas-Maraver Jesús, Kevrekidis Panayotis G
Mathematisch Instituut, Universiteit Leiden, P.O. Box 9512, 2300 RA Leiden, The Netherlands.
Grupo de Física No Lineal, Departamento de Física Aplicada I, Universidad de Sevilla, Escuela Politécnica Superior, C/Virgen de África, 7, 41011 Sevilla, Spain.
Entropy (Basel). 2024 Sep 4;26(9):756. doi: 10.3390/e26090756.
The existence of breather-type solutions, i.e., solutions that are periodic in time and exponentially localized in space, is a very unusual feature for continuum, nonlinear wave-type equations. Following an earlier work establishing a theorem for the existence of such structures, we bring to bear a combination of analysis-inspired numerical tools that permit the construction of such waveforms to a desired numerical accuracy. In addition, this enables us to explore their numerical stability. Our computations show that for the spatially heterogeneous form of the ϕ4 model considered herein, the breather solutions are generically unstable. Their instability seems to generically favor the motion of the relevant structures. We expect that these results may inspire further studies towards the identification of stable continuous breathers in spatially heterogeneous, continuum nonlinear wave equation models.
呼吸子型解的存在，即时间上周期且空间上指数局域化的解，对于连续的非线性波动方程而言是一个非常不寻常的特征。继早期建立此类结构存在性定理的工作之后，我们运用了一系列受分析启发的数值工具，这些工具能够将此类波形构建到所需的数值精度。此外，这使我们能够探究它们的数值稳定性。我们的计算表明，对于本文所考虑的空间非均匀形式的ϕ4模型，呼吸子解通常是不稳定的。它们的不稳定性似乎通常有利于相关结构的运动。我们期望这些结果可能会激发进一步的研究，以在空间非均匀的连续非线性波动方程模型中识别稳定的连续呼吸子。
