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Abstract <p> Contact germs are considered, transforming solutions of some partial differential equations into solutions of other equations. Parametric symmetries of differential equations are defined, generalizing point and contact symmetries. New transformations and symmetries can depend on derivatives of arbitrary but finite order. Stationary Schrödinger equations, as well as acoustics and gas dynamics equations, are regarded as examples. </p>

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Contact Germs and Their Application to Partial Differential Equations

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • O. V. Kaptsov

摘要

Abstract

Contact germs are considered, transforming solutions of some partial differential equations into solutions of other equations. Parametric symmetries of differential equations are defined, generalizing point and contact symmetries. New transformations and symmetries can depend on derivatives of arbitrary but finite order. Stationary Schrödinger equations, as well as acoustics and gas dynamics equations, are regarded as examples.