Fractional Klein-Gordon equation for linear dispersive phenomena: analytical methods and applications
Analysis of PDEs
2015-09-21 v2
Abstract
In this paper we discuss some exact results related to the fractional Klein--Gordon equation involving fractional powers of the D'Alembert operator. By means of a space-time transformation, we reduce the fractional Klein--Gordon equation to a fractional hyper-Bessel-type equation. We find an exact analytic solution by using the McBride theory of fractional powers of hyper-Bessel operators. A discussion of these results within the framework of linear dispersive wave equations is provided. We also present exact solutions of the fractional Klein-Gordon equation in the higher dimensional cases. Finally, we suggest a method of finding travelling wave solutions of the nonlinear fractional Klein-Gordon equation with power law nonlinearities.
Cite
@article{arxiv.1312.6019,
title = {Fractional Klein-Gordon equation for linear dispersive phenomena: analytical methods and applications},
author = {Roberto Garra and Enzo Orsingher and Federico Polito},
journal= {arXiv preprint arXiv:1312.6019},
year = {2015}
}