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Extension of the bilinear formalism to supersymmetric KdV-type equations

A S Carstea 2000 Nonlinearity 13 1645-1656   doi: 10.1088/0951-7715/13/5/312  Help

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A S Carstea
Institute of Physics and Nuclear Engineering, Department of Theoretical Physics, MG-6, Bucharest, Romania
E-mail: acarst@theor1.theory.nipne.ro

Recommended by A Kupiainen

Abstract. Extending the gauge-invariance principle for τ functions of the standard bilinear formalism to the supersymmetric case, we define Script N = 1 supersymmetric Hirota operators. Using them, we bilinearize SUSY KdV-type equations (KdV, Sawada-Kotera-Ramani). The supersoliton solutions and extension to SUSY sine-Gordon are also discussed. It is shown that the Lax-integrable SUSY KdV of the Mathieu equation does not possess an N-supersoliton solution for N≥3 for arbitrary parameters.The N-supersoliton solution only exists for a particular choice of parameters.

Mathematics Subject Classification: 37K10, 35Q51

Print publication: Issue 5 (September 2000)
Received 23 September 1999, in final form 17 May 2000

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