Hirota bilinear formalism and Supersymmetry

Details Hirota bilinear formalism and Supersymmetry Hirota bilinear formalism and Supersymmetry

2000-06-21

arxiv.org/abs/nlin/0006032v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

22 pages, no figures, to appear in Nonlinearity

Scientific paper

Extending the gauge-invariance principle for $\tau$ 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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