Article

Solution of the integro-differential wave equation with power-law nonlinearity

J. Sh. SafarovTashkent University of Information Technologies named after Muhammad Al-Khwarizmi

Izvestiya Instituta Matematiki i Informatiki Udmurt Gos Univjournal2026ru

ABI

Abstract

The behavior of a defocusing semilinear integro-differential equation of hyperbolic type with zero initial conditions is investigated. By introducing a new variable and new functions, the problem is reduced to a form convenient for analysis. Using integration over characteristics, the necessary conditions for the problem data are obtained. Next, using d'Alembert's formula, the problem is reduced to solving a Volterra-type integral equation. The existence and uniqueness of a solution to this problem are proven using the contraction mapping method.

Topics

Fractional Differential Equations Solutions Differential Equations and Boundary Problems advanced mathematical theories

Identifiers

DOI: 10.35634/2226-3594-2026-67-06

Citations and references

Cited by 00 references

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