General Solution of the Rayleigh Equation for the Description of Bubble Oscillations Near a Wall
We consider a generalization of the Rayleigh equation for the description of
the dynamics of a spherical gas bubble oscillating near an elastic or rigid wall. We show
that in the non–dissipative case, i.e. neglecting the liquid viscosity and compressibility, it
is possible to construct the general analytical solution of this equation. The corresponding
general solution is expressed via the Weierstrass elliptic function. We analyze the
dependence of this solution properties on the physical parameters.