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Zbl 0972.35521
Camassa, Roberto; Holm, Darryl D.
An integrable shallow water equation with peaked solitons. (English)
[J] Phys. Rev. Lett. 71, No.11, 1661-1664 (1993). ISSN 0031-9007; ISSN 1079-7114/e

Summary: 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.

MSC 2000:: *35Q51 Solitons
37K10 Completely integrable systems etc.
76B15 Wave motions (fluid mechanics)
76B25 Solitary waves, etc. (inviscid fluids)

Keywords: bi-Hamiltonian; conservation laws; asymptotic expansion; soliton solution

Cited in: Zbl 1176.65111 Zbl 1175.70001 Zbl 1080.35137 Zbl 1047.37047 Zbl 1090.37554

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