An integrable shallow water equation with linear and nonlinear dispersion - art. no. 194501

We use asymptotic analysis and a near-identity normal form transformation f rom water wave theory to derive a 1 + 1 unidirectional nonlinear wave equat ion that combines the linear dispersion of the Korteweg-deVries (KdV) equat ion with the nonlinear/nonlocal dispersion of the Camassa-Holtn (CH) equati on. This equation is one order more accurate in asymptotic approximation be yond KdV, yet it still preserves complete integrability via the inverse sca ttering transform method. Its traveling wave solutions contain both the KdV solitons and the CH peakons as limiting cases.