1995/04/18 by S. Baker, V. Z. Enolskii, V.Z. Enolskii +2 · 46 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Canonical transformation #Connection (principal bundle) #Hamiltonian (control theory) #Integrable system #Korteweg–de Vries equation #Lax pair #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #Quartic function #hep-th
paper · pdf · doi:10.1016/0375-9601(95)00267-7
published in Physics Letters A 201(2-3), 167-174 (Elsevier BV) · LaTex, 11 pages
arxiv created 1995/04/18 · openalex publication_date 1995/05/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We show a surprising connection between known integrable Hamiltonian systems with quartic potential and the stationary flows of some coupled KdV systems related to fourth order Lax operators. In particular, we present a connection between the Hirota-Satsuma coupled KdV system and (a generalisation of) the 1:6:1 integrable case quartic potential. A generalisation of the 1:6:8 case is similarly related to a different (but gauge related) fourth order Lax operator. We exploit this connection to derive a Lax representation for each of these integrable systems. In this context a canonical transformation is derived through a gauge transformation.