Infinite dimensional symmetry group, Kac-Moody-Virasoro algebras and integrability of Kac-Wakimoto equation

TL;DR

This paper investigates the integrability of a complex eighth-order (3+1)-dimensional equation, revealing an infinite-dimensional symmetry group with Virasoro-like structure, but it lacks the Painlevé property, and classifies its symmetry algebra.

Contribution

It introduces the symmetry analysis of a high-order multidimensional equation, identifying its infinite-dimensional symmetry algebra and its algebraic structure, which is novel in this context.

Findings

Symmetry group is infinite-dimensional with Virasoro-like structure.

The equation does not possess the Painlevé property.

Classifications of the symmetry algebra are provided.

Abstract

An eighth-order equation in (3+1)-dimension is studied for its integrability. Its symmetry group is shown to be infinite-dimensional and is checked for Virasoro like structure. The equation is shown not to have Painlev$\acute{\rm e}$ property. One and two-dimensional classifications of infinite-dimensional symmetry algebra is also given.