Abstract
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.
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