On the main problem in the theory of waves generated when a solid body is immersed in a liquid (ondes par emersion)

Abstract

The question related is reduced, as is known in mathematical physics, to the definition of a function ϕ (x, y, t), depending on the point (x, y) and on time t, which satisfies the following conditions (see article). It is absolutely clear, as M. Vergue notes in his interesting memoir, that the expansion theorem also holds for waves occurring under the influence of impulsive forces applied on the surface of the liquid (ondes par impulsion) - the only difference is that sin is replaced by cos in the formula.