New local and nonlocal conservation laws for evolution type equations

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Thesis Type: Doctorate

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

Approval Date: 2009

Thesis Language: Turkish

Student: EMRULLAH YAŞAR

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

Co-Supervisor: Teoman Özer

Abstract:

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.