Hirota bilinear formalism and Supersymmetry

arXivnlin/0006032MaRDI QIDQ6501625

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Abstract: Extending the gauge-invariance principle for $au$ functions of the standard bilinear formalism to the supersymmetric case, we define $calN=1$ 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 $Ngeq3$ for arbitrary parameters. Only for a particular choice of them the N super-soliton solution exists.

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