Integrability of one bilinear equation: singularity analysis and dimension

Abstract

The integrability of a four-dimensional sixth-order bilinear equation associated with the exceptional affine Lie algebra $D_4^{(1)}$ is studied by means of the singularity analysis. This equation is shown to pass the Painlevé test in three distinct cases of its coefficients, exactly when the equation is effectively a three-dimensional one, equivalent to the BKP equation.

8 pages; v2: one sentence corrected

References in corpus (6)

• KdV6: An Integrable System
• On integrability of the vector short pulse equation
• Integrability of Kersten-Krasil'shchik coupled KdV-mKdV equations: singularity analysis and Lax pair
• Enlarged spectral problems and nonintegrability
• Singularity analysis of a spherical Kadomtsev-Petviashvili equation
• Singularity Analysis and Integrability of a Burgers-Type System of Foursov

Cited by in corpus (1)

• On integrability of a third-order complex nonlinear wave equation