Abstract
The propagation of the optical solitons is usually governed by the nonlinear Schrodinger equations. In this article, the two variable(G'⁄G,1⁄G) -expansion method is employed to construct the exact traveling wave solutions with parameters of two nonlinear partial differential equations (PDEs) namely, the (1+1)-dimensional nonlinear Schrodinger-Boussinesq system and the (2+1)-dimensional hyperbolic nonlinear Schrodinger (HNLS) equation which describe the propagation of optical pulses in optic fibers. When the parameters are replaced by special values, the solitary wave solutions of these equations are found from the traveling waves. Key words: The two variable (G'⁄G,1⁄G) -expansion method, nonlinear Schrodinger-Boussinesq system, hyperbolic nonlinear Schrodinger (HNLS) equation, exact traveling wave solutions, solitary wave solutions.
Highlights
In the recent years, investigations of exact solutions to nonlinear partial differential equation (PDEs) play an important role in the study of nonlinear physical phenomena
GG ', G1 -expansion method is used in this article to obtain new exact solutions of two nonlinear
Schrödinger-Boussinesq system and the (2+1)dimensional hyperbolic nonlinear Schrödinger (HNLS) equation. These exact solutions are presented in terms of the hyperbolic, trigonometric and rational functions
Summary
Investigations of exact solutions to nonlinear partial differential equation (PDEs) play an important role in the study of nonlinear physical phenomena. G al., 2008; Zhang et al, 2008; Zayed and Gepreel, 2009; Zayed, 2009; Bekir, 2008; Ayhan and Bekir, 2012; Kudryashov, 2010a, b; Aslan, 2010; Zayed, 2010;), the ' -expansion method (Zhang et al, 2011), modified G. GG ' , G1 -expansion method (Li et al, 2010; Zayed and Abdelaziz, 2012; Zayed et al, 2012; Zayed and Alurrfi, 2014a, b), the Riccati equation method (Ma and Fuchssteiner, 1996), the bilinear method (Ma, 2011, 2013), the transformed rational function method
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