Construction of type-II Bäcklund transformation for the mKdV hierarchy

• Autor(a) principal: Gomes, J. F. [UNESP]
• Data de Publicação: 2015
• Outros Autores: Retore, A. L. [UNESP], Zimerman, A. H. [UNESP]
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://dx.doi.org/10.1088/1751-8113/48/40/405203; http://hdl.handle.net/11449/172075
• topic: Bäcklund transformation; integrable hierarchies; solitons

From an algebraic construction of the mKdV hierarchy we observe that the space component of the Lax operator plays the role of a universal algebraic object. This fact induces the universality of a gauge transformation that relates two field configurations of a given member of the hierarchy. Such gauge transformation generates the Bäcklund transformation (BT). In this paper we propose a systematic construction of BT for the entire mKdV hierarchy from the known type-II BT of the sinh-Gordon theory. We explicitly construct the BT of the first few integrable models associated to positive and negative grade-time evolutions. Solutions of these transformations for several cases describing the transition from vacuum-vacuum and the vacuum to one-soliton solutions which determines the value for the auxiliary field and the Bäcklund parameter respectively, independently of the model. The same follows for the scattering of two one-soliton solutions. The resultant delay is determined by a condition independent of the model considered.