Zero curvature and Gel'fand-Dikii formalisms

In soliton theory, integrable nonlinear partial differential equations play an important role. In that respect such differential equations create great interest in many research areas. There are several ways to obtain these differential equations; among them zero curvature and Gel’fand-Dikii formalisms are more effective. In this thesis, we studied these formalisms and applied them to explicit examples.