The Cauchy–Dirichlet Problem for the Relativistic Dirac Wave Equation
Tokibetov Z. Abduakhitova G. Kusherbayeva U.
June 2025Springer
Journal of Mathematical Sciences (United States)
2025#291Issue 1148 - 155 pp.
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.
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Al-Farabi Kazakh National University, 71, Al-Farabi Av, Almaty, 050040, Kazakhstan
Al-Farabi Kazakh National University
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