The Kac-Wakimoto Equation Is Not Integrable

2016/11/30 by Pekcan, Aslı
#Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences

paper · doi:10.48550/arxiv.1611.10254

Abstract

We study the (3+1)-dimensional eight-order nonlinear wave equation associated with the principal representation of the exceptional affine Lie algebra E₆⁽¹⁾, which was constructed by Kac and Wakimoto and stated that N-soliton solution of the equation can be formulated. We show that the equation is not Hirota integrable since it does not have three-soliton solution, even it has one- and two-soliton solutions.

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