Study of Bäcklund Transformations for Hierarchies KdV and mKdV
Bäcklund Transformations, Sólitons, Nonlinear equations.
In this thesis we present a study of the Bäcklund transformations for the hierarchies Korteweg - de Vries (KdV) and modied Korteweg - de Vries (mKdV). We show that it is possible to obtain a auto-Bäcklund transformation valid for all the equations that make up the KdV and mKdV hierarchies. For this, we use the Riccati system associated with each hierarchy and demonstrate, by mathematical induction, that it remains invariant under a given transformation. In addition, we use the auto-Bäcklund transformation to obtain the soliton solutions and the non-linear superposition formulas of each hierarchy.