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

Аннотация

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.

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DOI

10.35634/2226-3594-2026-67-06

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