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Bilinear approach to the supersymmetric Gardner equation

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Abstract

We study a supersymmetric version of the Gardner equation (both focusing and defocusing) using the superbilinear formalism. This equation is new and cannot be obtained from the supersymmetric modified Korteweg–de Vries equation with a nonzero boundary condition. We construct supersymmetric solitons and then by passing to the long-wave limit in the focusing case obtain rational nonsingular solutions. We also discuss the supersymmetric version of the defocusing equation and the dynamics of its solutions.

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Authors and Affiliations

  1. Department of Theoretical Physics, Institute of Physics and Nuclear Engineering, Bucharest, Romania

    C. N. Babalic & A. S. Carstea

  2. University of Craiova, Craiova, Romania

    C. N. Babalic & A. S. Carstea

Authors
  1. C. N. Babalic
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  2. A. S. Carstea
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Corresponding author

Correspondence to A. S. Carstea.

Additional information

The research of N. C. Babalic is supported by the Romanian Ministry of Education and Research (Project No. PN-II-ID-PCE-2011-3-0083).

The research of A. S. Carstea is supported by the Romanian Ministry of Education and Research (Project No. PN-II-ID-PCE-2011-3-0137).

Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 188, No. 2, pp. 244–253, August, 2016.

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Babalic, C.N., Carstea, A.S. Bilinear approach to the supersymmetric Gardner equation. Theor Math Phys 188, 1172–1180 (2016). https://doi.org/10.1134/S0040577916080031

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  • DOI: https://doi.org/10.1134/S0040577916080031

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