Bosonization of supersymmetric KdV equation |
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Authors: | Xiao Nan GaoSY Lou |
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Institution: | a Department of Physics, Shanghai Jiao Tong University, Shanghai, 200240, China b Faculty of Science, Ningbo University, Ningbo, 315211, China c School of Mathematics, Fudan University, Shanghai, 200433, China |
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Abstract: | Bosonization approach to the classical supersymmetric systems is presented. By introducing the multi-fermionic parameters in the expansions of the superfields, the N=1 supersymmetric KdV (sKdV) system is 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 is discovered. The rich multi-soliton solutions obtained here have not yet been obtained by using other methods. However, the traditional known multi-soliton solutions can also not be obtained by the bosonization approach of this Letter. Some open problems on the bosonization of the supersymmetric integrable models are proposed in the both classical and quantum levels. |
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