Abstract
Shallow water waves are studied using a nonlinear wave equation (W2) derived from Euler's equations by Whitham's method: W2 is the Korteweg--de Vries (KdV) equation plus higher-order correction terms. By projecting numerical simulations of W2 onto the soliton and radiation modes of the inverse scattering transform for the KdV equation we (i) generalize the soliton concept to higher order, (ii) provide a rigorous interpretation of a new soliton resonance effect, (iii) demonstrate that solitons and radiation undergo inelastic collisions, and (iv) find evidence for soliton creation and destruction.
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