Abstract
In this chapter, evolution of light beams in a cubic-quintic-septic-nonical medium is investigated. As the model equation, an extended form of the well-known nonlinear Schrödinger (NLS) equation is taken into account. By the use of a special ansatz, exact analytical solutions describing bright/dark and kink solitons are constructed. The existence of the wave solutions is discussed in a parameter regime. Moreover, the stability properties of the obtained solutions are investigated, and by employing Stuart and DiPrima’s stability analysis method, an analytical expression for the modulational stability is found.
Highlights
The study of spatial solitons in the field of fiber-optical communication has attracted considerable interest in recent years
The dynamics of spatial optical solitons is governed by the well-known nonlinear Schrödinger (NLS) equation
We have investigated the higher-order nonlinear Schrödinger equation involving nonlinearity up to the ninth order
Summary
The study of spatial solitons in the field of fiber-optical communication has attracted considerable interest in recent years. In the setting of nonlinear optics, a kink soliton represents a shock front that propagates undistorted inside the dispersive nonlinear medium [10] This type of solitons has been studied extensively, both analytically and numerically [11–13]. The cubic-quintic-nonlinear Schrödinger equation (CQNLSE) models materials with fifth-order susceptibility χð5Þ This kind of nonlinearity (cubicquintic CQ) is named as parabolic law nonlinearity and existing in nonlinear media such as the p-toluene sulfonate (PTS) crystals. This seeds several motivations to discover new features of solitons with combined effects of higher-order nonlinear parameters In this regard, Houria et al [28] constructed dark spatial solitary waves in a cubic-quintic-septic-nonlinear medium, with a profile in a functional form given in terms of “sech2=3”. The typical outcomes of the nonlinear development of the MI are reported
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