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Wave breaking for the nonlocal Whitham-type equations

  • Jian Chen
  • Shaojie Yang
  • Zhaoyang Yin
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Abstract

In this paper, we investigate wave breaking for the nonlocal Whitham-type equations. We establish more general wave breaking criteria that strictly extend earlier wave breaking criteria for the nonlocal Whitham-type equations. The approach relies on analyzing the monotonicity and continuity properties of a linear combination comprising the supremum and infimum of the solution's slope. Further generalizations are demonstrated via applications to the Camassa-Holm equation, the μ-Camassa-Holm equation and the hyperelastic rod equation. Our refined approach yields more precise wave breaking criteria, thereby extending the theoretical understanding of singularity formation in dispersive waves.

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Cite

BibTeXRIS
BibTeX
@misc{chen2026wave,
  title = {{Wave breaking for the nonlocal Whitham-type equations}},
  author = {Jian Chen and Shaojie Yang and Zhaoyang Yin},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.27832},
  eprint = {2610.27832},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.27832},
}
RIS
TY  - UNPB
TI  - Wave breaking for the nonlocal Whitham-type equations
AU  - Jian Chen
AU  - Shaojie Yang
AU  - Zhaoyang Yin
PY  - 2026
DA  - 2026/10/23
PB  - arXiv
DO  - 10.48550/arxiv.2610.27832
UR  - https://arxiv.org/abs/2610.27832
AB  - In this paper, we investigate wave breaking for the nonlocal Whitham-type equations. We establish more general wave breaking criteria that strictly extend earlier wave breaking criteria for the nonlocal Whitham-type equations. The approach relies on analyzing the monotonicity and continuity properties of a linear combination comprising the supremum and infimum of the solution's slope. Further generalizations are demonstrated via applications to the Camassa-Holm equation, the μ-Camassa-Holm equation and the hyperelastic rod equation. Our refined approach yields more precise wave breaking criteria, thereby extending the theoretical understanding of singularity formation in dispersive waves.
ER  -