An integrable shallow water equation with peaked solitons
Phys. Rev. Lett. 71, 1661 – Published 13 September, 1993
DOI: https://doi.org/10.1103/PhysRevLett.71.1661
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.