Hypercomplex analysis and integration of systems of ordinary differential equations |
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Authors: | Célestin Wafo Soh Fazal M Mahomed |
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Institution: | 1. Department of Mathematics and Statistical Sciences, Jackson State University JSU Box 17610, Jackson, USA;2. DST‐NRF Centre of Excellence in Mathematical and Statistical Sciences, School of Computer Science and Applied Mathematics, University of the Witwatersrand, Johannesburg, South Africa |
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Abstract: | We review the theory of hypercomplex numbers and hypercomplex analysis with the ultimate goal of applying them to issues related to the integration of systems of ordinary differential equations (ODEs). We introduce the notion of hypercomplexification, which allows the lifting of some results known for scalar ODEs to systems of ODEs. In particular, we provide another approach to the construction of superposition laws for some Riccati‐type systems, we obtain invariants of Abel‐type systems, we derive integrable Ermakov systems through hypercomplexification, we address the problem of linearization by hypercomplexification, and we provide a solution to the inverse problem of the calculus of variations for some systems of ODEs. Copyright © 2016 John Wiley & Sons, Ltd. |
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Keywords: | hypercomplex numbers hypercomplex analysis generalized complex numbers hypercomplexification base equation invariants superposition principle Lagrangian |
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