Bright, dark and W-shaped solitons with extended nonlinear Schrödinger's equation for odd and even higher-order terms

• Published in: Superlattices and microstructures Vol. 114; pp. 53 - 61
• Main Authors: Bendahmane, Issam, Triki, Houria, Biswas, Anjan, Saleh Alshomrani, Ali, Zhou, Qin, Moshokoa, Seithuti P., Belic, Milivoj
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.02.2018
• Subjects: Complex amplitude ansatz; Extended nonlinear Schrödinger equation; Higher-order dispersion; Solitary wave; Solitary wave; Higher-order dispersion; Complex amplitude ansatz; Extended nonlinear Schrödinger equation
• ISSN: 0749-6036; 1096-3677
• DOI: 10.1016/j.spmi.2017.12.007

We present solitary wave solutions of an extended nonlinear Schrödinger equation with higher-order odd (third-order) and even (fourth-order) terms by using an ansatz method. The including high-order dispersion terms have significant physical applications in fiber optics, the Heisenberg spin chain, and ocean waves. Exact envelope solutions comprise bright, dark and W-shaped solitary waves, illustrating the potentially rich set of solitary wave solutions of the extended model. Furthermore, we investigate the properties of these solitary waves in nonlinear and dispersive media. Moreover, specific constraints on the system parameters for the existence of these structures are discussed exactly. The results show that the higher-order dispersion and nonlinear effects play a crucial role for the formation and properties of propagating waves. •An extended nonlinear Schrödinger equation with higher-order odd and even terms is studied.•Properties of solitary waves in nonlinear and dispersive media are discussed.•Bright, dark and W-shaped solitons are reported.