AI 中文总结
通过数值模拟系统研究mKdV方程呼吸子解，证明其在多种扰动下稳定，并扩展至对称势的不可积情形，提供数值证据表明其可长期保持稳定。
AI 中文摘要
我们通过数值模拟系统研究了修正Korteweg-de Vries（mKdV）方程中的呼吸子解。我们表明，呼吸子解在各种扰动下是稳定的，包括振幅变化、内部参数的修改以及方程非线性项的扰动。我们的结果不仅与已知的关于可积系统中呼吸子稳定性的解析研究一致，并进一步扩展了这些研究，而且还提供了数值证据，表明在具有对称势的某些不可积设置中，此类呼吸子型结构可以在模拟的时间尺度内持续存在并保持稳定。
英文摘要
We systematically investigate breather solutions in the modified Korteweg-de Vries (mKdV) equation via numerical simulations. We show that the breather solutions are stable under a variety of perturbations, including amplitude changes, modifications of internal parameters, and perturbations of the nonlinearity of the equation. Our results are not only consistent with the known analytical studies on the stability of breathers in integrable systems, extending them further, but also provide numerical evidence that such breather-type structures can persist and remain stable over the simulated time scales in some non-integrable settings with symmetric potentials.
Commentsappeared in "Studies in Applied Math", 31 pages, 30 figures
Journal refStudies in Applied Math, 157 (2026): e70263
