Discretizing families of linearizable equations |
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| Institution: | 2. CPT, Ecole Polytechnique, CNRS, UPR 14, 91128 Palaiseau, France;3. CRM, Université de Montréal, CP 6127, succ. Centre-ville, Montréal, H3C 3J7 Canada;1. Department of Informatics & Telecommunications, National and Kapodistrian University of Athens, Greece;2. ATHENA Research & Innovation Center, Maroussi, Greece;3. Université Cote d''Azur, Inria Méditerranée, Project Team Aromath, Sophia-Antipolis, France;4. Sorbonne Université, CNRS, INRIA, Laboratoire d''Informatique de Paris 6, LIP6, Équipe PolSys, 4 place Jussieu, F-75005, Paris, France;1. BCAM — Basque Center for Applied Mathematics, Alameda de Mazarredo 14, 48009 Bilbao, Basque Country, Spain;2. Johann Bernoulli Institute, University of Groningen, Nijenborgh 9, 9747 AG, Groningen, The Netherlands;1. Laboratory of Information Technologies, Joint Institute for Nuclear Research, 6 Joliot-Curie St, Dubna, 141980, Russian Federation;2. Russian Federation and Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation;3. Department of Electrical Engineering and Computer Science, Ostwestfalen-Lippe University of Applied Sciences, Liebigstraße 87, 32657 Lemgo, Germany;4. School of Computing, Electronics and Mathematics, Plymouth University, 2-5 Kirkby Place, Drake Circus, Plymouth, PL4 8AA, United Kingdom |
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| Abstract: | We investigate generalizations of the discrete Riccati equation as a linearizable system, to multicomponent linearizable systems. These are discretizations of nonlinear ordinary differential equations with superposition formulas. We present discrete matrix Riccati equations, projective, conformal, orthogonal and symplectic Riccati equations. Also obtained are discrete equations, based on complex orthogonal and symplectic groups, that in the continuous limit involve fourth order polynomial nonlinearities. All these equations satisfy the criterion of singularity confinement. |
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