Construction of type-II Backlund transformation for the mKdV hierarchy

Autor(es)

Gomes, J. F. ^[1] ; Retore, A. L. ^[1] ; Zimerman, A. H. ^[1]

Afiliação do(s) autor(es)

^[1] Inst Fis Teor UNESP, BR-01140070 Sao Paulo - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of Physics A-Mathematical and Theoretical; v. 48, n. 40 OCT 9 2015.
• Citações Web of Science: 2

Resumo

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 Backlund 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 Backlund 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. (AU)

• Processo FAPESP: 15/00025-9 - Transformações de Backlund em hierarquias integráveis, sólitons e defeitos integráveis
• Beneficiário: Ana Lúcia Retore
• Modalidade de apoio: Bolsas no Brasil - Doutorado