The deformation method and the Bäcklund Transformations

The Bäcklund Transformations were developed in 1875 (Bäcklund, A. V., Lund Univ. Arsskrift 10 1875, Bäcklund, A. V., Math. Ann. 9 297 1876), as a mathematical tool used in the related theories of differential geometry and differential equations, to construct Multi-Soliton solutions. In this work we show a different procedure to determine Multi-Solitons solutions, by applying an approach based on the deformation method or BLM map, introduced in the literature by Bazeia, Losano and Malbouisson (D. Bazeia, L. Losano, J. M. C. Malbouisson, Phys. Review D 66 (2002) 101701), where their main objective was to obtain new classes of analytical topological defects for scalar field theory. Our idea still under construction, but shows an interest connection between some well known integrable models, such as Sine Gordon and the KdV equations.