Cylindrical solitons in shallow water of variable depth

Summary The propagation and the interaction of cylindrical solitons in shallow vater of variable depth are studied. Starting from the cylindrically symmetric version of the equations describing long waves in a beach, a Korteweg-de Vries equation type ψ_τ+6ψψ_ξ+ψ_ξξξ=−Γ(τ)ψ is derived. Since no exact analytical solution has been found to date for this equation, some remarkable cases in which the equation takes up a tractable form are analysed. Finally the interaction between cylindrical imploding and expanding waves is considered and the phase shifts caused by the head-on collision are given. This work was supported by CNR-GNFM.