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Abstract <p> In a neighborhood of a cuspidal caustic, the Maslov canonical operator can be represented as a linear combination of the composite Pearcey function and its derivatives with coefficients that are smooth functions independent of the small parameter of the asymptotics. This representation plays an important role when constructing asymptotic solutions of various equations describing wave propagation (such as the wave equation, Maxwell equations, and linearized shallow water equations). The paper provides a method for writing computationally efficient formulas for these coefficients, thus extending the preceding research in this direction. </p>

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On the Coefficients of the Pearcey Function and Its Derivatives in a Representation of the Canonical Operator near a Cuspidal Caustic

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • V.E. Nazaikinskii

摘要

Abstract

In a neighborhood of a cuspidal caustic, the Maslov canonical operator can be represented as a linear combination of the composite Pearcey function and its derivatives with coefficients that are smooth functions independent of the small parameter of the asymptotics. This representation plays an important role when constructing asymptotic solutions of various equations describing wave propagation (such as the wave equation, Maxwell equations, and linearized shallow water equations). The paper provides a method for writing computationally efficient formulas for these coefficients, thus extending the preceding research in this direction.