A nonlinear wave equation associated with a nonlinear integral equation

Abstract

Motivated by the well-posedness results in [Nonlinear Anal. Ser. B: RWA. 4(3) (2003), 483, 501; Nonlinear Anal. Ser. B: RWA. 11(5) (2010), 3453-3462] for the models describing the propagation of high frequency electromagnetic waves in nonlinear dielectric media, because of their mathematical context, we study a similar model and prove results about existence, uniqueness, the asymptotic behavior and an asymptotic expansion of the solution up to order N in a small parameter λ with error λ^{N+½}