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<p>In this article, we investigate the integrability nature of a modified form of coupled sextic anharmonic oscillators using the Painlevé analysis for ordinary differential equations. We observe that the considered system is a Lagrangian system, and our analysis reveals that the system is integrable for a set of three distinct parametric conditions. For each of the isolated parametric conditions, we find a pair of non-point symmetries and obtain time-dependent integrals by applying Noether’s theorem. From our analysis, we infer that the modified coupled sextic anharmonic oscillators are integrable for the identified set of three different parametric values.</p>

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On the integrability of a modified coupled sextic anharmonic oscillators

  • 期刊论文

  • 发表日期：

    2026年6月23日

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  • C. Uma Maheswari,
  • N. Muthuchamy

摘要

In this article, we investigate the integrability nature of a modified form of coupled sextic anharmonic oscillators using the Painlevé analysis for ordinary differential equations. We observe that the considered system is a Lagrangian system, and our analysis reveals that the system is integrable for a set of three distinct parametric conditions. For each of the isolated parametric conditions, we find a pair of non-point symmetries and obtain time-dependent integrals by applying Noether’s theorem. From our analysis, we infer that the modified coupled sextic anharmonic oscillators are integrable for the identified set of three different parametric values.