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Published online by Cambridge University Press: 11 April 2006
Approximations for shallow-water ship waves are sought which are valid near the critical speed U = (gh)1/2. For sufficiently thin bodies (struts or ships) the governing equation is dispersive. Simple analytic solutions are given which are valid for all F2 ≤ O(1). As the thickness increases, nonlinearity also enters. A soliton solution is discussed which applies to a sharp-nosed half-body at slightly supercritical speed.