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<p>Given a PDE, in [E. López-González, E. A. Martínez-García, and R. Torres-Córdoba, <i>Chaos Solitons Fractals</i>, <b>73</b>, Article 113757 (2023)], the authors proposed a method for the construction of solutions by considering an associative real algebra A and a suitable affine vector field φ with respect to which the components of all functions ℒ <i>○</i> φ are solutions, where ℒ is differentiable in Lorch’s sense with respect to 𝔸<i>.</i> If we consider the 3D cyclic algebra and a suitable 3D affine map φ<i>,</i> then we get families of solutions for the Laplace equation with three independent variables.</p>

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Potentials for Solenoidal Fields Using the Three-Dimensional φ-Harmonic Cyclic Algebra

  • 期刊论文

  • 发表日期：

    2025年4月1日

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  • Homero G. Díaz-Marín,
  • Elifalet López-González,
  • Osvaldo Osuna

摘要

Given a PDE, in [E. López-González, E. A. Martínez-García, and R. Torres-Córdoba, Chaos Solitons Fractals, 73, Article 113757 (2023)], the authors proposed a method for the construction of solutions by considering an associative real algebra A and a suitable affine vector field φ with respect to which the components of all functions ℒ ○ φ are solutions, where ℒ is differentiable in Lorch’s sense with respect to 𝔸. If we consider the 3D cyclic algebra and a suitable 3D affine map φ, then we get families of solutions for the Laplace equation with three independent variables.