Semantic Apparatus – Classification of singular differential invariants in (1 + 3)-dimensional space and integrability

Cited by Lee Sonogan

Classification of singular differential invariants in (1+3)-dimensional  space and integrability - Muhammad Ayub, Zahida Sultan, Muhammad Naeem  Qureshi, Fazal Mahmood Mahomed, 2021

Abstract by Muhammad Ayub, Zahida Sultan, Muhammad Naeem Qureshi, …

Singularity is one of the important features in invariant structures in several physical phenomena reflected often in the associated invariant differential equations. The classification problem for singular differential invariants in (1+3)-dimensional space associated with Lie algebras of dimension 4 is investigated. The formulation of singular invariants for a Lie algebra of dimension 4 possessed by the underlying system of three second-order ordinary differential equations is studied in detail and the corresponding canonical forms for these systems are deduced. Furthermore, the categorization of singular invariants on the basis of conditional singularity, weak uncoupling, weak linearization, partial uncoupling and partial linearization are described for the underlying canonical forms. In addition, those cases of classified canonical forms are also mentioned which do not lead to singular invariant systems of three second-order ODEs for a Lie algebra of dimension 4. The integrability aspect of these classified singular-invariant systems in (1+3)-dimensional space is discussed in a detailed manner for a Lie algebra of dimension 4. Finally, two physical systems from mechanics are presented to illustrate the utilization of the physical aspect of these singular invariants.

Publication: Science Progress (sagepub.com(Peer-Reviewed Journal)

Pub Date: Dec 1, 2021 Doi: https://journals.sagepub.com/doi/full/10.1177/00368504211054258

Keywords: Systems of second-order ODEs, singular invariant equations, conditional singularity, integrability, Lie algebra

https://journals.sagepub.com/doi/full/10.1177/00368504211054258 (Plenty more sections and references in this research)

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