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Natural extension of a Lie algebra A4,18b,|b|≤1, realizations, invariant systems and integrability

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  • Ayub, Muhammad
  • Bano, Saira

Abstract

In the frame of Lie theory, the classical successive reduction of order for scalar ODEs is not much effective for system of differential equations due to technical hurdles. Lie algebraic approach is utilized to overcome these hurdles, then further invoked for the classification, linearization and integrability of system of differential equations. But in the case of higher dimension, this approach has also its own limitations due to classification of low dimensional Lie algebras and corresponding realizations. In the realm of Lie algebra theory, a natural extension refers to the process that involves enlarging a Lie algebra by adding new elements or structures while maintaining the fundamental algebraic properties. This extension technique finds applications in various fields, including physics, geometry, and mathematics.

Suggested Citation

  • Ayub, Muhammad & Bano, Saira, 2025. "Natural extension of a Lie algebra A4,18b,|b|≤1, realizations, invariant systems and integrability," Applied Mathematics and Computation, Elsevier, vol. 494(C).
    • Handle: RePEc:eee:apmaco:v:494:y:2025:i:c:s0096300325000013
    DOI: 10.1016/j.amc.2025.129274
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    References listed on IDEAS

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    1. Muhammad Ayub & Masood Khan & F. M. Mahomed, 2013. "Second‐Order Systems of ODEs Admitting Three‐Dimensional Lie Algebras and Integrability," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    2. S. Zahida & M. N. Qureshi & Muhammad Ayub, 2017. "Canonical Forms and Their Integrability for Systems of Three 2nd‐Order ODEs," Advances in Mathematical Physics, John Wiley & Sons, vol. 2017(1).
    3. Muhammad Ayub & Masood Khan & F. M. Mahomed, 2013. "Second-Order Systems of ODEs Admitting Three-Dimensional Lie Algebras and Integrability," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-15, April.
    4. Ayub, Muhammad & Sadique, Sadia & Mahomed, F.M., 2016. "Singular invariant structures for Lie algebras admitted by a system of second-order ODEs," Applied Mathematics and Computation, Elsevier, vol. 281(C), pages 137-147.
    5. S. Zahida & M. N. Qureshi & Muhammad Ayub, 2017. "Canonical Forms and Their Integrability for Systems of Three 2nd-Order ODEs," Advances in Mathematical Physics, Hindawi, vol. 2017, pages 1-12, July.
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