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Hypercomplex analysis and integration of systems of ordinary differential equations
Author(s) -
Soh Célestin Wafo,
Mahomed Fazal M.
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3852
Subject(s) - mathematics , ode , integrable system , ordinary differential equation , hypercomplex number , bernoulli differential equation , linearization , type (biology) , scalar (mathematics) , algebra over a field , mathematical analysis , differential equation , pure mathematics , differential algebraic equation , nonlinear system , ecology , physics , geometry , quantum mechanics , biology , quaternion
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.