Eur. Phys. J. Plus (2016) 131: 97
https://doi.org/10.1140/epjp/i2016-16097-3

Regular Article

Abundant soliton solutions for the coupled Schrödinger-Boussinesq system via an analytical method

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

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

Received: 25 January 2016
Revised: 23 February 2016
Accepted: 27 February 2016
Published online: 15 April 2016

Abstract

In this paper, the improved tan-expansion method is proposed to find the exact soliton solutions of the coupled Schrödinger-Boussinesq (SB) system. The exact particular solutions are of five types: hyperbolic function solution (exact soliton wave solution), trigonometric function solution (exact periodic wave solution), rational exponential solution (exact singular kink-type wave solution), logarithmic solution and rational solution (exact singular cupson wave solution). We obtained the further solutions comparing with other methods. The results demonstrate that the new tan-expansion method is more efficient than the Ansatz method applied by Bilige et al. (2013). Recently this method was developed for searching the exact travelling-wave solutions of nonlinear partial differential equations. Abundant exact travelling-wave solutions including solitons, kink, periodic and rational solutions have been found. These solutions might play an important role in Laser and plasma. It is shown that this method, with the help of symbolic computation, provides a straightforward and powerful mathematical tool for solving the nonlinear problems.