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Abstract <p> We obtain necessary and sufficient conditions for Darboux integrability of hyperbolic partial differential equations that admit non-autonomic first-order integrals along one of the characteristics. Based on these conditions, we find a family of Darboux integrable equations, which is probably new. </p>

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On Darboux integrable equations with non-autonomous first-order integrals

  • 期刊论文

  • 发表日期：

    2025年11月25日

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  • S. Ya. Startsev

摘要

Abstract

We obtain necessary and sufficient conditions for Darboux integrability of hyperbolic partial differential equations that admit non-autonomic first-order integrals along one of the characteristics. Based on these conditions, we find a family of Darboux integrable equations, which is probably new.