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<p>We construct three- and four-dimensional generalizations of the Cauchy–Riemann system and a first order hyperbolic system of four independent variables. We prove that each component of the vector solution is a solution to the four-dimensional wave equation. We find a solution to the Cauchy–Dirichlet problem for the relativistic wave system of Dirac equations in an explicit form. Then we get a first order system for a fourdimensional vector-valued function, each component of which is a solution to the wave equation. We show that the solution is representable as a series.</p>

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The Cauchy–Dirichlet Problem for the Relativistic Dirac Wave Equation

  • 期刊论文

  • 发表日期：

    2025年6月7日

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  • Zhanuzak Tokibetov,
  • Gulzhan Abduakhitova,
  • Ulbike Kusherbayeva

摘要

We construct three- and four-dimensional generalizations of the Cauchy–Riemann system and a first order hyperbolic system of four independent variables. We prove that each component of the vector solution is a solution to the four-dimensional wave equation. We find a solution to the Cauchy–Dirichlet problem for the relativistic wave system of Dirac equations in an explicit form. Then we get a first order system for a fourdimensional vector-valued function, each component of which is a solution to the wave equation. We show that the solution is representable as a series.