Lineer Olmayan Kısmi Diferansiyel Denklemlerin Backlund Dönüşümleri
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In this thesis, it is studied how the B¨acklund transformations of nonlinear partial differential equations are obtained and deriving new solutions from the known solutions by using these transformations with the superposition formulas obtained via the permutability conditions of the equations. Particularly, for some nonlinear partial differential equations which are well known in mathematical physics, the importance of B¨acklund transformations is emphasized by showing that one can derive N-solitons from 1-soliton solutions. For this purpose, Hirota D-operator and Hirota method that are used to obtain B¨acklund transformations are also explained. Within this context Korteweg-de Vries (KdV), Sine-Gordon (SG) and Boussinesq equations are analyzed in detail.