Aerial plane waves of finite amplitude

Abstract

In the investigations which follow, we are concerned with the motion of an elastic fluid in one dimension, say, parallel to x . It is implied not only that there are no component velocities perpendicular to x , but that the motion is the same in any perpendicular plane, so that it is a function of x and of the time ( t ) only. If u be the velocity at any point x, p the pressure, ρ the density, X an impressed force, the dynamical equation for an inviscid fluid is du/dt + u du/dx = X - 1/ ρ dp/dx . At the same time the "equation of continuity" takes the form dρ/dt + d (pu)/dx = 0.