SOLITON CREATION AND DESTRUCTION, RESONANT INTERACTIONS, AND INELASTIC-COLLISIONS IN SHALLOW-WATER WAVES

Shallow water waves are studied using a nonlinear wave equation (W2) d erived from Euler's equations by Whitham's method: W2 is the Korteweg- de Vries (KdV) equation plus higher-order correction terms. By project ing numerical simulations of W2 onto the soliton and radiation modes o f the inverse scattering transform for the KdV equation we (i) general ize the soliton concept to higher order, (ii) provide a rigorous inter pretation of a new soliton resonance effect, (iii) demonstrate that so litons and radiation undergo inelastic collisions, and (iv) find evide nce for soliton creation and destruction. [S0031-9007(98)07500-0].