Hydrodynamic Foundation and Painlevé Analysis of Hirota-Satsuma-Type Equations

Abstract

In this communication the Painlevé-Weiss (PW) analysis is applied to Hirota-Satsuma-type equations, and the hydrodynamic foundation of such equations is presented. It is found that among all the equations of this kind, only the original Hirota-Satsuma eq., and the equation due to Ablowitz, Kaup, Newell and Segur, possess the PW property.