New approximate-analytical solutions for the nonlinear fractional Schr\"{o}dinger equation with second-order spatio-temporal dispersion via double Laplace transform method
General Mathematics
2020-10-22 v1
Abstract
In this paper, a modified nonlinear Schr\"{o}dinger equation with spatio-temporal dispersion is formulated in the senses of Caputo fractional derivative and conformable derivative. A new generalized double Laplace transform coupled with Adomian decomposition method has been defined and applied to solve the newly formulated nonlinear Schr\"{o}dinger equation with spatio-temporal dispersion. The approximate analytical solutions using the proposed generalized method in the sense of Caputo fractional derivative and conformable derivatives are obtained and compared with each other graphically.
Keywords
Cite
@article{arxiv.2010.10977,
title = {New approximate-analytical solutions for the nonlinear fractional Schr\"{o}dinger equation with second-order spatio-temporal dispersion via double Laplace transform method},
author = {Mohammed K. A. Kaabar and Francisco Martínez and José Francisco Gómez-Aguilar and Behzad Ghanbari and Melike Kaplan},
journal= {arXiv preprint arXiv:2010.10977},
year = {2020}
}
Comments
19 pages, 10 figures, 1 table, submitted to Optik journal, Elsevier