Eur. Phys. J. Plus (2017) 132: 494
https://doi.org/10.1140/epjp/i2017-11762-7

Regular Article

Applications of the ETEM for obtaining optical soliton solutions for the Lakshmanan-Porsezian-Daniel model

¹ Young Researchers and Elite Club, Ilkhchi Branch, Islamic Azad University, Ilkhchi, Iran
² Department of Mathematics, Payame Noor University, PO BOX 19395-3697, Tehran, Iran
³ Department of Mathematics, Ahar Branch, Islamic Azad University, Ahar, Iran

^* e-mail: j_manafianheris@tabrizu.ac.ir

Received: 1 September 2017
Accepted: 27 October 2017
Published online: 28 November 2017

Abstract

This paper examines the effectiveness of an integration scheme which is called the extended trial equation method (ETEM) for solving a well-known nonlinear equation of partial differential equations (PDEs). In this respect, the Lakshmanan-Porsezian-Daniel (LPD) equation with Kerr and power laws of nonlinearity which describes higher-order dispersion, full nonlinearity and spatiotemporal dispersion is considered, and as an achievement, a series of exact travelling-wave solutions for the aforementioned equation is formally extracted. Explicit new exact solutions are derived in different form such as dark solitons, bright solitons, solitary wave, periodic solitary wave, rational function, and elliptic function solutions of LPD equation. The movement of obtained solutions is shown graphically, which helps to understand the physical phenomena of this optical soliton equation. Many other such types of nonlinear equations arising in basic fabric of communications network technology and nonlinear optics can also be solved by this method.