Artículos de revistas
Construction of type-II Bäcklund transformation for the mKdV hierarchy
Fecha
2015-09-14Registro en:
Journal of Physics A: Mathematical and Theoretical, v. 48, n. 40, 2015.
1751-8121
1751-8113
10.1088/1751-8113/48/40/405203
2-s2.0-84941759199
2-s2.0-84941759199.pdf
8215976645016606
Autor
Universidade Estadual Paulista (Unesp)
Institución
Resumen
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.