On optical solitons of the Schrödinger-Hirota equation with power law nonlinearity in optical fibers

Aslan, Ebru Cavlak; Tchier, Fairouz; Inc, Mustafa

doi:10.1016/j.spmi.2017.03.014

Cited by 74 publications

(8 citation statements)

References 16 publications

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“…Certainly, any investigation in this research area would be helpful in understanding complex dynamical phenomena (see, e.g. [30,31]) in dispersive wave theories.…”

Section: Discussionmentioning

confidence: 99%

Linear superposition of Wronskian rational solutions to the KdV equation

Ma¹

2021

Commun. Theor. Phys.

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A linear superposition is studied for Wronskian rational solutions to the KdV equation, which include rogue wave solutions. It is proved that it is equivalent to a polynomial identity that an arbitrary linear combination of two Wronskian polynomial solutions with a difference two between the Wronskian orders is again a solution to the bilinear KdV equation. It is also conjectured that there is no other rational solutions among general linear superpositions of Wronskian rational solutions.

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“…Certainly, any investigation in this research area would be helpful in understanding complex dynamical phenomena (see, e.g. [30,31]) in dispersive wave theories.…”

Section: Discussionmentioning

confidence: 99%

Linear superposition of Wronskian rational solutions to the KdV equation

Ma¹

2021

Commun. Theor. Phys.

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“…Due to the method of solution, which makes use of elliptic functions, these functions will expand the set of solutions that can be given to polynomial nonlinear equations, in general [8,[12][13][14][15][16][17][18][19][20][21][22][23][24][25].…”

Section: Remarksmentioning

confidence: 99%

Three Solutions to the Nonlinear Schrödinger Equation for a Constant Potential

Vega¹

2019

Nonlinear Optics - Novel Results in Theory and Applications

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We introduce three sets of solutions to the nonlinear Schrödinger equation for the free particle case. A well-known solution is written in terms of Jacobi elliptic functions, which are the nonlinear versions of the trigonometric functions sin, cos, tan, cot, sec, and csc. The nonlinear versions of the other related functions like the real and complex exponential functions and the linear combinations of them is the subject of this chapter. We also illustrate the use of these functions in Quantum Mechanics as well as in nonlinear optics.

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“…[2,9] Previously, the propagation dynamics of beams were well discussed through numerical simulation [10] or inverse scattering modeling and so on. [11] In recent years, people often use Jacobi elliptic function, [12] variable separation method, [13] variational method (VM), [14][15][16] and other integration algorithms to solve relevant problems. Moreover, some properties of beams in propagation process have been verified in many aspects, such as nonlocalization in dispersion shock wave, [17] Anderson localization, [18] gradient mutation, guide wave distribution coupling, and photon condensation.…”

Section: Introductionmentioning

confidence: 99%

Propagation dynamics of dipole breathing wave in lossy nonlocal nonlinear media

Guo¹,

Yang²,

Li³

et al. 2022

Chinese Phys. B

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In the framework of nonlinear wave optics, we report the evolution process of a dipole breathing wave in lossy nonlocal nonlinear media based on the nonlocal nonlinear Schrödinger equation. The analytical expression of the dipole breathing wave in such a nonlinear system is obtained by using the variational method. Taking advantage of the analytical expression, we analyze the influences of various physical parameters on the breathing wave propagation, including the propagation loss and the input power on the beam width, the beam intensity, and the wavefront curvature. Also, the corresponding analytical solutions are obtained. The validity of the analysis results is verified by numerical simulation. This study provides some new insights for investigating beam propagation in lossy nonlinear media

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On optical solitons of the Schrödinger-Hirota equation with power law nonlinearity in optical fibers

Cited by 74 publications

References 16 publications

Linear superposition of Wronskian rational solutions to the KdV equation

Linear superposition of Wronskian rational solutions to the KdV equation

Three Solutions to the Nonlinear Schrödinger Equation for a Constant Potential

Propagation dynamics of dipole breathing wave in lossy nonlocal nonlinear media

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