1999/08/31 by V. B. Kuznetsov, V B Kuznetsov, M. Salerno +3 · 67 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Eigenfunction #Integrable system #Matrix (chemical analysis) #Monodromy #Monodromy matrix #Monomial #Nonlinear Waves and Solitons #Polynomial #Quantum #Quantum Mechanics and Non-Hermitian Physics #TRACE (psycholinguistics) #Transformation (genetics) #hep-th #math.CA #math.QA #nlin.SI #solv-int
paper · pdf · doi:10.1088/0305-4470/33/1/311
published in Journal of Physics A Mathematical and General 33(1), 171-189 (Institute of Physics) · 24 pages, corrected refs to Sections and a misprint
arxiv created 1999/09/27 · openalex publication_date 1999/12/15 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
For the integrable case of the discrete self-trapping (DST) model we construct a Bäcklund transformation. The dual Lax matrix and the corresponding dual Bäcklund transformation are also found and studied. The quantum analogue of the Bäcklund transformation ( Q -operator) is constructed as the trace of a monodromy matrix with an infinite-dimensional auxiliary space. We present the Q -operator as an explicit integral operator as well as describing its action on the monomial basis. As a result we obtain a family of integral equations for multivariable polynomial eigenfunctions of the quantum integrable DST model. These eigenfunctions are special functions of the Heun class which is beyond the hypergeometric class. The integral equations found are new and they shall provide a basis for efficient analytical and numerical studies of such complicated functions.