Punctured Lagrangian manifolds and asymptotic solutions of the linear water wave equations with localized initial conditions

摘要

Is localized at the initial time in a domain of linear dimensions of the order of μ in a neighborhood of a point x_0, the vertical velocities at that time being zero in view of the first equation in (1). (Conditions of this kind are used, say, in the piston model of tsunami wave generation; e.g., see [2].)