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Robustness of mKdV Breathers: A Numerical Perspective

  • Chandler Haight
  • Svetlana Roudenko
  • Diana Son
  • Kai Yang
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Abstract

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.

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Cite

BibTeXRIS
BibTeX
@misc{haight2026robustness,
  title = {{Robustness of mKdV Breathers: A Numerical Perspective}},
  author = {Chandler Haight and Svetlana Roudenko and Diana Son and Kai Yang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.27080},
  eprint = {2609.27080},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.27080},
}
RIS
TY  - UNPB
TI  - Robustness of mKdV Breathers: A Numerical Perspective
AU  - Chandler Haight
AU  - Svetlana Roudenko
AU  - Diana Son
AU  - Kai Yang
PY  - 2026
DA  - 2026/09/22
PB  - arXiv
DO  - 10.48550/arxiv.2609.27080
UR  - https://arxiv.org/abs/2609.27080
AB  - 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.
ER  -