An integrable shallow water equation with peaked solitons

Roberto Camassa and Darryl D. Holm
Phys. Rev. Lett. 71, 1661 – Published 13 September 1993
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Abstract

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.

  • Received 18 May 1993

DOI:https://doi.org/10.1103/PhysRevLett.71.1661

©1993 American Physical Society

Authors & Affiliations

Roberto Camassa and Darryl D. Holm

  • Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545

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Issue

Vol. 71, Iss. 11 — 13 September 1993

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