2001/02/22 by Anatol Odzijewicz, A. Odzijewicz, A. Ryzko +1 · 7 citations
Mathematics · Physics and Astronomy · #Action (physics) #Algebraic Riccati equation #Algebraic structures and combinatorial models #Applied mathematics #Class (philosophy) #Computer science #Differential equation #Integrable system #Mathematical analysis #Mathematics #Nonlinear Waves and Solitons #Physics #Pure mathematics #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #Riccati equation #math-ph #math.MP
paper · pdf · doi:10.1088/0305-4470/35/3/318
published in Journal of Physics A Mathematical and General 35(3), 747-757 (Institute of Physics) · 11 pages LATEX
arxiv created 2001/02/22 · openalex publication_date 2002/01/14 · arxiv updated 2013/11/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Using the q -version of the Darboux transform we obtain the general solution of q -difference Riccati equation from a special one by the action of one-parameter group. This allows us to construct the solutions for the large class of q -difference Riccati equations as well as q -difference Schrödinger equations, which are different from those obtained by the standard Darboux transform.