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<p>By investigating the invariant algebraic curves whose cofactors are the divergence of the system multiplied by an integer, we obtain the necessary and sufficient conditions for polynomial Rayleigh–Duffing systems (except Liénard systems) to have elementary first integrals. It is shown that rewriting the polynomial equation of the invariant algebraic curve as a Weierstrass polynomial equation is useful.</p>

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Elementary Integrability of Polynomial Rayleigh–Duffing Systems

  • 期刊论文

  • 发表日期：

    2024年12月31日

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  • Jiashuang Yu,
  • Jun Zhang

摘要

By investigating the invariant algebraic curves whose cofactors are the divergence of the system multiplied by an integer, we obtain the necessary and sufficient conditions for polynomial Rayleigh–Duffing systems (except Liénard systems) to have elementary first integrals. It is shown that rewriting the polynomial equation of the invariant algebraic curve as a Weierstrass polynomial equation is useful.