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 ${\mathfrak{e}}_6^{(1)}$. Using the Painlevé 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.

7 pages

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