Aerial plane waves of finite amplitude

Source abstract

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/ρdp/dx. At the same time the "equation of continuity" takes the form dρ/dt + d (pu)/dx = 0.