Nonlinear time-fractional dispersive equations
Abstract
In this paper we study some cases of time-fractional nonlinear dispersive equations (NDEs) involving Caputo derivatives, by means of the invariant subspace method. This method allows to find exact solutions to nonlinear time-fractional partial differential equations by separating variables. We first consider a third order time-fractional NDE that admits a four-dimensional invariant subspace and we find a similarity solution. We also study a fifth order NDE. In this last case we find a solution involving Mittag-Leffler functions. We finally observe that the invariant subspace method permits to find explicit solutions for a wide class of nonlinear dispersive time-fractional equations.
Cite
@article{arxiv.1410.8085,
title = {Nonlinear time-fractional dispersive equations},
author = {P. Artale Harris and R. Garra},
journal= {arXiv preprint arXiv:1410.8085},
year = {2014}
}
Comments
14 pages; in press in Communications in Applied and Industrial Mathematics (2014)