标题： 超对称KdV方程的玻色化 显示英文标题

标题： Bosonization of Supersymmetric KdV equation

摘要： 玻色化方法用于经典超对称系统。通过在超场展开中引入多费米子参数，将$\mathcal {N}=1$超对称 KdV（sKdV）方程转化为一组耦合的玻色方程。该方法可以应用于任何费米子系统。通过求解耦合的玻色方程，可以显式地获得一些新颖类型的精确解。特别是，发现了超对称可积系统的局域激发的丰富性。这里获得的丰富多孤子解尚未通过其他方法获得。不幸的是，传统的已知多孤子解也无法通过本文的玻色化方法获得。在经典和量子层次上，提出了一些关于超对称可积模型玻色化的一些开放问题。 显示英文摘要

摘要： 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.