2015/05/05 by J. F. Gomes, Ana L. Retore, A. L. Retore +2 · 11 citations
Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic number #Algebraic structure #Algebraic structures and combinatorial models #Field (mathematics) #Gauge theory #Hierarchy #Integrable system #Lax pair #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Nonlinear system #Operator (biology) #Physics #Pure mathematics #Quantum mechanics #Soliton #Transformation (genetics) #Universality (dynamical systems) #hep-th #math-ph #math.MP #nlin.SI
paper · pdf · doi:10.1088/1751-8113/48/40/405203
published in Journal of Physics A Mathematical and Theoretical 48(40), 405203 (Institute of Physics) · latex 21 pages
arxiv created 2015/05/05 · openalex publication_date 2015/09/14 · arxiv updated 2015/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.