Exact soliton solution for the fourth‐order nonlinear Schrödinger equation with generalized cubic‐quintic nonlinearity

Abstract

In this paper, we investigate the fourth‐order nonlinear Schrödinger equation with parameterized nonlinearity that is generalized from regular cubic‐quintic formulation in optics and ultracold physics scenario. We find the exact solution of the fourth‐order generalized cubic‐quintic nonlinear Schrödinger equation through modified F‐expansion method, identifying the particular bright soliton behavior under certain external experimental setting, with the system's particular nonlinear features demonstrated. Copyright © 2016 John Wiley & Sons, Ltd.

Solitary waves described by a high‐order system in optical fiber Bragg gratings with arbitrary refractive index

“…We cannot find an exact solution of the system of Equations ( 9)- (10) in this case. Therefore, we introduce the limitations…”

“…[1][2][3][4][5][6][7][8] The basic equation for constructing such mathematical models is the Schrödinger equation. [9][10][11][12][13][14][15][16] Beyond that, coupled systems of nonlinear Schrödinger equations [17][18][19][20][21] are studied. The type of optical fiber is also taken into account in the construction of mathematical models.…”

“…At the present, the study of pulse propagation in optical fibers is of great interest 1–8 . The basic equation for constructing such mathematical models is the Schrödinger equation 9–16 . Beyond that, coupled systems of nonlinear Schrödinger equations 17–21 are studied.…”

Soliton solution of high‐order nonlinear Schrödinger equation based on ansatz method

“…We all know that the research on soliton is now not only in the laboratory stage. With the wide application of soliton in various emerging industries, such as communication and conduction, people's research on it has become more and more in depth (see previous studies [5][6][7][8][9][10][11][12][13] ). Similarly, it is precisely because of this wide application prospect that scholars cannot stand still in their research on it.…”