Integrability Study of a Four-dimensional Eighth-order Nonlinear Wave Equation

Abstract

We study the integrability of the four-dimensional eighth-order nonlinear wave equation of Kac and Wakimoto, associated with the exceptional affine Lie algebra e (1) 6 . Using the Painlev´e analysis for partial differential equations, we show that this equation must be non-integrable in the Lax sense but very likely it possesses a lower-order integrable reduction.