https://doi.org/10.1140/epjp/i2016-16166-7
Regular Article
Soliton solutions to a few fractional nonlinear evolution equations in shallow water wave dynamics
1
Department of Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran
2
Department of Mathematics, Faculty of Science and Arts, Bozok University, 66100, Yozgat, Turkey
3
Department of Physics, Faculty of Science, Erciyes University, 38039, Kayseri, Turkey
4
Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran
5
Department of Mathematical Sciences, Delaware State University, 19901-2277, Dover, DE, USA
6
Department of Mathematics, King Abdulaziz University, 21589, Jeddah, Saudi Arabia
* e-mail: ekici-m@hotmail.com
Received:
23
January
2016
Revised:
8
April
2016
Accepted:
16
April
2016
Published online:
25
May
2016
This paper studies a few nonlinear evolution equations that appear with fractional temporal evolution and fractional spatial derivatives. These are Benjamin-Bona-Mahoney equation, dispersive long wave equation and Nizhnik-Novikov-Veselov equation. The extended Jacobi’s elliptic function expansion method is implemented to obtain soliton and other periodic singular solutions to these equations. In the limiting case, when the modulus of ellipticity approaches zero or unity, these doubly periodic functions approach solitary waves or shock waves or periodic singular solutions emerge.
© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg, 2016
