New local and nonlocal conservation laws for evolution type equations

Thesis Type: Doctorate

Institution Of The Thesis: Bursa Uludağ University, Fen Bilimleri Enstitüsü, Mathematics, Turkey

Approval Date: 2009

Thesis Language: Turkish


Principal Supervisor (For Co-Supervisor Theses): Sibel Yalçın Tokgöz

Co-Supervisor: Teoman Özer


In this doctoral thesis, we study the local and nonlocal conservation laws ofevolution type equations. It is demonstrated that there exist local or nonlocalconservation laws for each symmetry (Lie point, Lie-Backlund and nonlocal symmetry)of evolution type equations which have not Lagrangians. We also obtain potentialsymmetries , symmetry reductions and invariant solutions by utilizing conservationlaws. In addition, symmetry classifications were constructed for in question equationswhich have arbitrary functions.