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<p>We consider the problem of constructing a quasiclassical variational functional for a one-dimensional homogeneous wave equation in a pentagon-shaped domain. Using the variational method for hyperbolic equations proposed by V.&#xa0;M.&#xa0;Filippov, we obtain a variational functional involving line and iterated integrals in the characteristic variables. This form of the variational functional is adapted for training neural networks that approximate solutions of boundary-value problems in mathematical physics, and increases the efficiency and speed of learning.</p>

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ON QUASICLASSICAL VARIATIONAL FUNCTIONALS FOR THE WAVE EQUATION

  • 期刊论文

  • 发表日期：

    2026年2月1日

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  • S. G. Shorokhov

摘要

We consider the problem of constructing a quasiclassical variational functional for a one-dimensional homogeneous wave equation in a pentagon-shaped domain. Using the variational method for hyperbolic equations proposed by V. M. Filippov, we obtain a variational functional involving line and iterated integrals in the characteristic variables. This form of the variational functional is adapted for training neural networks that approximate solutions of boundary-value problems in mathematical physics, and increases the efficiency and speed of learning.