New types of exact solutions for the fourth-order dispersive cubic–quintic nonlinear Schrödinger equation

• Published in: Applied mathematics and computation Vol. 217; no. 12; pp. 5967 - 5971
• Main Author: Xu, Gui-Qiong
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 15.02.2011; Elsevier
• Subjects: Exact sciences and technology; Global analysis, analysis on manifolds; Mathematical analysis; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Numerical linear algebra; Partial differential equations; Periodic wave solution; Sciences and techniques of general use; Soliton solution; Special functions; The nonlinear Schrödinger equation; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds; Soliton solution; The nonlinear Schrödinger equation; Periodic wave solution; Numerical linear algebra; Periodic solution; Schrödinger equation; Exact solution; Non linear equation; Direct method; Numerical analysis; Linear system; Matrix inversion; Applied mathematics; Algebraic method; Nonlinearity; Analytical solution
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2010.12.008

In this study, we use two direct algebraic methods to solve a fourth-order dispersive cubic–quintic nonlinear Schrödinger equation, which is used to describe the propagation of optical pulse in a medium exhibiting a parabolic nonlinearity law. By using complex envelope ansatz method, we first obtain a new dark soliton and bright soliton, which may approach nonzero when the time variable approaches infinity. Then a series of analytical exact solutions are constructed by means of F-expansion method. These solutions include solitary wave solutions of the bell shape, solitary wave solutions of the kink shape, and periodic wave solutions of Jacobian elliptic function.