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Hirota bilinear formalism and Supersymmetry

A. S. Carstea
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Abstract

Extending the gauge-invariance principle for $τ$ functions of the standard bilinear formalism to the supersymmetric case, we define ${\cal N}=1$ supersymmetric Hirota bilinear operators. Using them we bilinearize supersymmetric nonlinear evolution equations. The super-soliton solutions are discussed. As a quite strange paradox it is shown that the Lax integrable supersymmetric KdV of Manin-Radul-Mathieu equation does not possesses N super-soliton solution for $N\geq 3$ for arbitrary parameters. Only for a particular choice of them the N super-soliton solution exists.

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A. S. Carstea. 2000-06-21. Hirota bilinear formalism and Supersymmetry. https://arxiv.org/abs/nlin/0006032

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