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On the supersymmetric nonlinear evolution equations

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Abstract

Supersymmetrization of a nonlinear evolution equation in which the bosonic equation is independent of the fermionic variable and the system is linear in fermionic field goes by the name B-supersymmetrization. We provide B-supersymmetric extension of a number of quasilinear and fully nonlinear evolution equations and demonstrate that the supersymmetric system follows from the usual action principle. We observe that B-supersymmetrization can also be realized using a generalized Noetherian symmetry such that the resulting set of Lagrangian symmetries coincides with symmetries of the field equations. Following this viewpoint we derive conservation laws for the supersymmetric pair of equations. We attempt to realize the bosonic and fermionic fields in terms of bright and dark solitons. The interpretation sought by us has its origin in the classic work of Bateman who introduced a reverse-time system with negative friction to bring linear dissipative systems within the framework of variational principle.

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Authors and Affiliations

  1. Department of Physics, Visva-Bharati University, Santiniketan, 731235, India

    Amitava Choudhuri & B. Talukdar

  2. Patha Bhavana, Visva-Bharati University, Santiniketan, 731235, India

    S. Ghosh

Authors
  1. Amitava Choudhuri
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  2. B. Talukdar
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  3. S. Ghosh
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Correspondence to B. Talukdar.

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Choudhuri, A., Talukdar, B. & Ghosh, S. On the supersymmetric nonlinear evolution equations. Nonlinear Dyn 58, 249–258 (2009). https://doi.org/10.1007/s11071-009-9475-2

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  • DOI: https://doi.org/10.1007/s11071-009-9475-2

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