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Bosonization, singularity analysis, nonlocal symmetry reductions and exact solutions of supersymmetric KdV equation

  • Xiao Nan Gao
  • S. Y. LouEmail author
  • Xiao Yan Tang
Article

Abstract

Assuming that there exist at least two fermionic parameters, the classical \( \mathcal{N}=1 \) supersymmetric Korteweg-de Vries (SKdV) system can be transformed to some coupled bosonic systems. The boson fields in the bosonized SKdV (BSKdV) systems are defined on even Grassmann algebra. Due to the intrusion of other Grassmann parameters, the BSKdV systems are different from the usual non-supersymmetric integrable systems, and many more abundant solution structures can be unearthed. With the help of the singularity analysis, the Painlevé property of the BSKdV system is proved and a Bäcklund transformation (BT) is found. The BT related nonlocal symmetry, we call it as residual symmetry, is used to find symmetry reduction solutions of the BSKdV system. Hinted from the symmetry reduction solutions, a more generalized but much simpler method is established to find exact solutions of the BSKdV and then the SKdV systems, which actually can be applied to any fermionic systems.

Keywords

Integrable Equations in Physics Integrable Hierarchies Supersymmetric Effective Theories 

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Copyright information

© SISSA, Trieste, Italy 2013

Authors and Affiliations

  1. 1.Department of PhysicsShanghai Jiao Tong UniversityShanghaiChina
  2. 2.Shanghai Key Laboratory of Trustworthy ComputingEast China Normal UniversityShanghaiChina
  3. 3.Faculty of ScienceNingbo UniversityNingboChina

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