Bosonization Procedure For Pure Integrable Fermionic Systems

In this paper, the bosonization procedure of the supersymmetric systems and theinverse version of the bosonization procedure (the fermionization approach) are studiedfor the supersymmetric systems. In the second chapter of the thesis, by means of thebosonization procedure of the supersymmetric systems, the N=1supersymmetricMKdV equation is transformed to a system of coupled bosonic equations. By solvingthe coupled bosonic equations, some novel types of exact solutions can be explicitly ob-tained. For simplicity, the exact solutions of the sMKdV equations are discussed for thecases of2-,3-and n-fermionic parameters. In the further study of the bosonization pro-cedure, the inverse version of the bosonization procedure (the fermionization approach)has been proposed. In the third chapter of the thesis, by studying a four-boson sys-tem with arbitrary parameters, we find some possible integrable bosonic systems andthe supersymmetric systems under some diferent senses. Furthermore, Some typesof special exact solutions of the supersymmetric extensions are obtained. Here, wetake the Sharma-Tasso-Olver (STO) equation and the burgers equation as illustrationexamples.