Analytical solution for the Rayleigh–Plesset equation by Weierstrass elliptic equation

The nonlinear dynamics of cavitation bubbles are studied theoretically through the Rayleigh–Plesset equation. A direct approach is first proposed to construct an analytical solution for cavitation bubbles. In particular, when considering the gas bubbles, we show the connection between the bubble motion and Weierstrass elliptic equation with the help of Sandman transformation. To the best of our knowledge, this is the first time that an elliptic function has been used to construct the parametric analytical solution for this case. The present findings would be significant in understanding the complex behavior of cavitation bubbles in practical applications, especially when considering the surface tension.