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 D4(1) is studied by means of the singularity analysis. This equation is shown to pass the Painlev\'e test in three distinct cases of its coefficients, exactly when the equation is effectively a three-dimensional one, equivalent to the BKP equation.
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