Pramana

, Volume 77, Issue 3, pp 581–594

Linearization of systems of four second-order ordinary differential equations

Article

Abstract

In this paper we provide invariant linearizability criteria for a class of systems of four second-order ordinary differential equations in terms of a set of 30 constraint equations on the coefficients of all derivative terms. The linearization criteria are derived by the analytic continuation of the geometric approach of projection of two-dimensional systems of cubically semi-linear second-order differential equations. Furthermore, the canonical form of such systems is also established. Numerous examples are presented that show how to linearize nonlinear systems to the free particle Newtonian systems with a maximally symmetric Lie algebra relative to \(sl(6, \Re)\) of dimension 35.

Keywords

Linearization geometric projections maximally symmetric complex Newtonian systems 

PACS No.

11.30.−j 

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Copyright information

© Indian Academy of Sciences 2011

Authors and Affiliations

  1. 1.Centre for Advanced Mathematics and PhysicsNational University of Sciences and TechnologyIslamabadPakistan
  2. 2.School of Electrical Engineering and Computer ScienceNational University of Sciences and TechnologyIslamabadPakistan
  3. 3.Centre for Differential Equations, Continuum Mechanics and Applications, School of Computational and Applied MathematicsUniversity of the WitwatersrandWitsSouth Africa

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