We study a class of 1+1 quadratically nonlinear water wave equations that
combines the linear dispersion of the Korteweg-deVries (KdV) equation with the
nonlinear/nonlocal dispersion of the Camassa-Holm (CH) equation, yet still
preserves integrability via the inverse scattering transform (IST) method.
This IST-integrable class of equations contains both the KdV equation and the
CH equation as limiting cases. It arises as the compatibility condition for a
second order isospectral eigenvalue problem and a first order equation for the
evolution of its eigenfunctions. This integrable equation is shown to be a
shallow water wave equation derived by asymptotic expansion at one order higher
approximation than KdV. We compare its traveling wave solutions to KdV
solitons.Comment: 4 pages, no figure
