Asymptotics of the convolution of the Airy function and a function of the power-like behavior
Analysis of PDEs
2015-11-11 v1
Abstract
The asymptotic behavior of the convolution-integral of a special form of the Airy function and a function of the power-like behavior at infinity is obtained. The integral under consideration is the solution of the Cauchy problem for an evolutionary third-order partial differential equation used in the theory of wave propagation in physical media with dispersion. The obtained result can be applied to studying asymptotics of solutions of the KdV equation by the matching method.
Keywords
Cite
@article{arxiv.1511.03021,
title = {Asymptotics of the convolution of the Airy function and a function of the power-like behavior},
author = {Sergei V. Zakharov},
journal= {arXiv preprint arXiv:1511.03021},
year = {2015}
}
Comments
Keywords: Airy function, convolution, Cauchy problem, asymptotics. 8 pages