Nonlinear optics problem with~transformation of a spatial variable and an oblique derivative

A. A. Kornuta ; V. A. Lukianenko

Contemporary Mathematics. Fundamental Directions, Contemporary Mathematics. Fundamental Directions, Tome 69 (2023) no. 2, pp. 276-288.

Résumé

In this paper, we consider a functional differential equation of parabolic type on a strip with a transformation of a spatial variable and boundary conditions with an oblique derivative. Using the Laplace and Fourier transforms, we obtain a representation of the problem under consideration in the form of a nonlinear integral equation. A special case of this representation is considered. The proved statements make it possible to implement iterative methods for obtaining approximate solutions of nonlinear partial differential equations taking into account the given conditions. The results show that the presented method is promising for solving similar problems.

Détail

Keywords: functional differential equations, boundary conditions with an oblique derivative
Mots-clés : bifurcation, Fourier transform, Laplace transform.

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