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Abstract <p> A reduction method using additive, multiplicative, and functional separation of variablesis applied to a hyperbolic equation with the Monge–Ampère operator. We obtainmultidimensional exact solutions expressed in closed form via elementary and special functionsand/or solutions of ordinary differential equations. Examples of exact solutions anisotropic withrespect to the spatial variables are given.</p>

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On Multidimensional Exact Solutions of a Hyperbolic Equation with the Monge–Ampère Operator

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • A. A. Kosov,
  • E. I. Semenov

摘要

Abstract

A reduction method using additive, multiplicative, and functional separation of variablesis applied to a hyperbolic equation with the Monge–Ampère operator. We obtainmultidimensional exact solutions expressed in closed form via elementary and special functionsand/or solutions of ordinary differential equations. Examples of exact solutions anisotropic withrespect to the spatial variables are given.