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An integrable shallow water equation with peaked solitons
Open accessAbstract
We derive a new completely integrable dispersive shallow water equation that is bi-Hamiltonian and thus possesses an infinite number of conservation laws in involution. The equation is obtained by using an asymptotic expansion directly in the Hamiltonian for Euler's equations in the shallow water regime. The soliton solution for this equation has a limiting form that has a discontinuity in the first derivative at its peak.
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Cited by
Making sense of non-Hermitian Hamiltonians
Bender, C. M. (2007) · Reports on Progress in Physics · doi:10.1088/0034-4885/70/6/r03 · Cited by 2,984
The Euler–Poincaré Equations and Semidirect Products with Applications to Continuum Theories
Holm, D. D., Marsden, J. E., & Ratiu, T. S. (1998) · Advances in Mathematics · doi:10.1006/aima.1998.1721 · Cited by 964
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Metadata
- Authors
- Camassa, R., & Holm, D. D.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1993-09-13
- Volume
- 71
- Issue
- 11
- Pages
- 1661-1664
- ISSN
- 0031-9007 (ISSN-L)
- OpenAlex
- W2026031976
- Cited by
- 3,624
- References
- 0
- FWCI
- 7.62
- Type
- journal article
- Language
- en
- Open access
- green
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- Camassa, R., & Holm, D. D. (1993). An integrable shallow water equation with peaked solitons. Physical Review Letters. https://doi.org/10.1103/physrevlett.71.1661
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