Soliton-like pulses governed by fourth order dispersion in optical fibers

Karlsson, Magnus; Höök, Anders

doi:10.1016/0030-4018(94)90560-6

Cited by 131 publications

(75 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…It will offer the guarantee for the transmission of communication in theory, and provide the developmental direction for searching the next generation carriers of communication. The solutions in this paper cannot be degenerated into the bright and dark solitary wave solutions in lower order dispersive nonlinear Schrödinger equations, [9][10][11][12] which suggests that the HNLSE (1) richly possesses other possible solutions worthy of further study. Although these solutions only represent a small subset of the large variety of possible solutions admitted by this higher-order nonlinear Schrödinger equation (1), those presented here are different from the ones in Refs.…”

Section: Discussionmentioning

confidence: 91%

Optical Solitary Wave Solutions for the Fourth-Order Dispersive Cubic-Quintic Nonlinear Schrödinger Equation

Dai

Chen

Zhang

2007

Int. J. Mod. Phys. B

View full text Add to dashboard Cite

We present several kinds of optical solitary wave solutions for the fourth-order dispersive cubic-quintic nonlinear Schrödinger equation describing the propagation of optical pulses in a medium that exhibits a parabolic nonlinearity law. Among them, apart from some regular fundamental bright solitary wave solutions and dark solitary wave solutions given, there are also two kinds of combined solitary wave solutions, i.e., bright and dark solitary wave and W-shaped solitary wave solutions which describe bright and dark solitary wave properties. It is found that their amplitude may approach nonzero when the time variable approaches infinity. Moreover, when the parameters of the bright and dark solitary wave are selected appropriately, the kink and anti-kink solitary wave solutions, which are first reported in the fourth-order dispersive cubic-quintic nonlinear Schrödinger equation, are discovered.

show abstract

Section: Discussionmentioning

confidence: 91%

Optical Solitary Wave Solutions for the Fourth-Order Dispersive Cubic-Quintic Nonlinear Schrödinger Equation

Dai

Chen

Zhang

2007

Int. J. Mod. Phys. B

View full text Add to dashboard Cite

show abstract

“…Another nonlinearity is F (u,u,ü, ... u ) = ±u 3 , then equation (1) is called the Extended Fischer-Kolmogorov equation or the Swift-Hohenberg equation see [5,15], and in other places, see for instance the book [26] and [2,7].…”

Section: Introduction and Statement Of The Main Resultsmentioning

confidence: 99%

Limit cycles for a class of fourth-order differential equations

Llibre

Sellami

Makhlouf

2009

Applicable Analysis

View full text Add to dashboard Cite

show abstract

“…The 1D solitons have been investigated relatively well, in microscopic model [14] as well as in macroscopic one [20] while the 3D case was too complicated for numerics (too time consuming). We also note that we do not expect that the 3D case can bring qualitative differences with the 2D case.…”

Section: Numericsmentioning

confidence: 99%