Melnikov's method in String Theory
  Melnikov's method is an analytical way to show the existence of classical chaos generated by a Smale horseshoe. It is a powerful technique, though its applicability is somewhat limited. In this paper, we present a solution of type IIB supergravity to which Melnikov's method is applicable. This is a brane-wave type deformation of the AdS$_5\times$S$^5$ background. By employing two reduction ans\"atze, we study two types of coupled pendulum-oscillator systems. Then the Melnikov function is computed for each of the systems by following the standard way of Holmes and Marsden and the existence of chaos is shown analytically. 
Yuhma Asano, Hideki Kyono and Kentaroh Yoshida
hep-th nlin.CD