Bosonization of Supersymmetric KdV equation

Abstract

Bosonization approach to the classical supersymmetric systems is presented. By introducing the multi-fermionic parameters in the expansions of the superfields, the $\mathcal{N}=1$ supersymmetric KdV (sKdV) equations are transformed to a system of coupled bosonic equations. The method can be applied to any fermionic systems. By solving the coupled bosonic equations, some novel types of exact solutions can be explicitly obtained. Especially, the richness of the localized excitations of the supersymmetric integrable system are discovered. The rich multi-soliton solutions obtained here have not yet been obtained by using other methods. Unfortunately, the traditional known multi-soliton solutions can also not be obtained by the bosonization approach of this paper. Some open problems on the bosonization of the supersymmetric integrable models are proposed in the both classical and quantum levels.

16 pages, 0 figure

References in corpus (2)

• Hidden supersymmetry in quantum bosonic systems
• A supersymmetric Sawada-Kotera equation

Cited by in corpus (10)

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• Bäcklund-Darboux Transformations and Discretizations of $N=2a=-2$ Supersymmetric KdV Equation
• On a set of Grassmann-valued extensions of systems of ordinary differential equations
• New negative grade solitonic sector for supersymmetric KdV and mKdV hierarchies
• Hamiltonian structure of an operator valued extension of Super KdV equations