Eur. Phys. J. Plus (2017) 132: 421
https://doi.org/10.1140/epjp/i2017-11681-7

Regular Article

Applications of IBSOM and ETEM for solving the nonlinear chains of atoms with long-range interactions

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

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

Received: 21 August 2017
Accepted: 28 August 2017
Published online: 13 October 2017

Abstract

This paper presents a number of new solutions obtained for solving a complex nonlinear equation describing dynamics of nonlinear chains of atoms via the improved Bernoulli sub-ODE method (IBSOM) and the extended trial equation method (ETEM). The proposed solutions are kink solitons, anti-kink solitons, soliton solutions, hyperbolic solutions, trigonometric solutions, and bellshaped soliton solutions. Then our new results are compared with the well-known results. The methods used here are very simple and succinct and can be also applied to other nonlinear models. The balance number of these methods is not constant contrary to other methods. The proposed methods also allow us to establish many new types of exact solutions. By utilizing the Maple software package, we show that all obtained solutions satisfy the conditions of the studied model. More importantly, the solutions found in this work can have significant applications in Hamilton’s equations and generalized momentum where solitons are used for long-range interactions.