Linearization criteria for a system of second-order quadratically semi-linear ordinary differential equations |
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| Authors: | F M Mahomed Asghar Qadir |
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| Institution: | (1) Centre for Differential Equations, Continuum Mechanics and Applications, School of Computational and Applied Mathematics, University of the Witwatersrand, Wits 2050, Johannesberg, South Africa;(2) Centre for Advanced Mathematics and Physics, National University of Sciences and Technology, Campus of the College of Electrical and Mechanical Engineering, Peshawar Road, Rawalpindi, Pakistan;(3) Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia |
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| Abstract: | Conditions are derived for the linearizability via invertible maps of a system of n second-order quadratically semi-linear differential equations that have no lower degree lower order terms in them, i.e.,
for the symmetry Lie algebra of the system to be sl(n + 2, ℝ). These conditions are stated in terms of the coefficients of the equations and hence provide simple invariant criteria
for such systems to admit the maximal symmetry algebra. We provide the explicit procedure for the construction of the linearizing
transformation. In the simplest case of a system of two second-order quadratically semi-linear equations without the linear
terms in the derivatives, we also provide the construction of the linearizing point transformation using complex variables.
Examples are given to illustrate our approach for two- and three-dimensional systems. |
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| Keywords: | Lie symmetry algebra Linearization System of second-order ordinary differential equations |
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