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<p>We study the problem of construction and classifying of common invariant solutions for the (1+3)-dimensional Euler–Lagrange–Born–Infeld and homogeneous Monge–Ampère equations. Some common invariant solutions of these equations obtained from the invariant solutions of the Euler–Lagrange–Born–Infeld equation and the classification of low-dimensional (dim<i>L</i> ≤ 3) nonconjugate subalgebras of the Lie algebra of the Poincaré group <i>P</i>(1,4) are presented and classified.</p>

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On the Construction and Classification of Common Invariant Solutions for the (1+3)-Dimensional Euler–Lagrange–Born–Infeld Equations and Homogeneous Monge–Ampère Equations

  • 期刊论文

  • 发表日期：

    2026年5月19日

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  • V. M. Fedorchuk,
  • V. I. Fedorchuk

摘要

We study the problem of construction and classifying of common invariant solutions for the (1+3)-dimensional Euler–Lagrange–Born–Infeld and homogeneous Monge–Ampère equations. Some common invariant solutions of these equations obtained from the invariant solutions of the Euler–Lagrange–Born–Infeld equation and the classification of low-dimensional (dimL ≤ 3) nonconjugate subalgebras of the Lie algebra of the Poincaré group P(1,4) are presented and classified.