Bilen, Ergün2016-01-082016-01-082012http://hdl.handle.net/11693/15707Ankara : The Department of Mathematics and the Graduate School of Engineering and Science of Bilkent University, 2012.Thesis (Master's) -- Bilkent University, 2012.Includes bibliographical refences.Recursion operators, if they exist, of nonlinear partial differential equations map symmetries to symmetries of these equations. It is this property that the integrable nonlinear partial differential equations possess infinitely many symmetries. In this work we studied two other properties of recursion operators. We shall use the recursion operators as Lax operators in the Gelfand-Dikii formalism and to classify certain integrable equations.vii, 79 leavesEnglishinfo:eu-repo/semantics/openAccesssymmetriesGelfand-Dikii formalismrecursion operatorclassificationQA372 .B54 2012Differential equations, Nonlinear.Symmetry (Physics)Recursion theory.Thesis