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Extension of the bilinear formalism to supersymmetric KdV-type equations

A S Carstea

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Recommended by A Kupiainen

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.


PACS

02.30.Ik Integrable systems

02.30.Jr Partial differential equations

02.30.Tb Operator theory

02.30.Sa Functional analysis

05.45.Yv Solitons

MSC

37K10 Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.)

35Q51 Solitons (See also 37K40)

35Q53 KdV-like equations (Korteweg-de Vries, Burgers, sine-Gordon, sinh-Gordon, etc.) (See also 37K10)

Subjects

Mathematical physics

Statistical physics and nonlinear systems

Dates

Issue 5 (September 2000)

Received 23 September 1999, in final form 17 May 2000



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