An integrable shallow water equation with peaked solitons

1993/05/13 by Roberto Camassa, Darryl D. Holm · 7 citations
Physics and Astronomy · #nlin.PS #patt-sol

paper · pdf · doi:10.1103/physrevlett.71.1661

LaTeX file. Figure available from authors upon request

arxiv created 1993/05/13 · arxiv updated 2009/11/30

Abstract

We derive a new completely integrable dispersive shallow water equation that is biHamiltonian 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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