Soliton solutions to coupled higher‐order nonlinear Schrödinger equations

1992 ◽  
Vol 33 (3) ◽  
pp. 1208-1215 ◽  
Author(s):  
R. S. Tasgal ◽  
M. J. Potasek
Keyword(s):  
Soliton Solutions ◽  
Higher Order ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations

N-dark–dark solitons for the coupled higher-order nonlinear Schrödinger equations in optical fibers

2017 ◽  
Vol 31 (33) ◽  
pp. 1750305 ◽  
Author(s):  
Hai-Qiang Zhang ◽  
Yue Wang
Keyword(s):  
Optical Fibers ◽  
Soliton Solutions ◽  
Dark Soliton ◽  
Higher Order ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Dark Solitons ◽  
Nonlinear Schrodinger Equations

In this paper, we construct the binary Darboux transformation on the coupled higher-order dispersive nonlinear Schrödinger equations in optical fibers. We present the N-fold iterative transformation in terms of the determinants. By the limit technique, we derive the N-dark–dark soliton solutions from the non-vanishing background. Based on the obtained solutions, we find that the collision mechanisms of dark vector solitons exhibit the standard elastic collisions in both two components.

Explode-Decay Solitons in the Generalized Inhomogeneous Higher-Order Nonlinear Schrödinger Equations

2007 ◽  
Vol 62 (7-8) ◽  
pp. 381-386 ◽  
Author(s):  
Ramaswamy Radha ◽  
V. Ramesh Kumar
Keyword(s):  
Gauge Transformation ◽  
Spin System ◽  
Soliton Solutions ◽  
Higher Order ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations ◽  
Multisoliton Solutions

In this paper we investigate the generalized inhomogeneous higher-order nonlinear Schrödinger equations, generated recently by deforming the inhomogeneous Heisenberg ferromagnetic spin system through a space curve formalism [Phys. Lett. A 352, 64 (2006)] and construct their multisoliton solutions, using gauge transformation. The amplitude of the bright soliton solutions generated grows and decays with time, and there is an exchange of energy between soliton trains during interaction.

scholarly journals Peregrine Solitons of the Higher-Order, Inhomogeneous, Coupled, Discrete, and Nonlocal Nonlinear Schrödinger Equations

2020 ◽  
Vol 8 ◽  
Author(s):  
T. Uthayakumar ◽  
L. Al Sakkaf ◽  
U. Al Khawaja
Keyword(s):  
Soliton Solutions ◽  
Analytical Techniques ◽  
Higher Order ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Nonlinear Saturation ◽  
Nonlinear Schrödinger ◽  
Historical Perspectives ◽  
Nonlinear Schrodinger Equations

This study reviews the Peregrine solitons appearing under the framework of a class of nonlinear Schrödinger equations describing the diverse nonlinear systems. The historical perspectives include the various analytical techniques developed for constructing the Peregrine soliton solutions, followed by the derivation of the general breather solution of the fundamental nonlinear Schrödinger equation through Darboux transformation. Subsequently, we collect all forms of nonlinear Schrödinger equations, involving systematically the effects of higher-order nonlinearity, inhomogeneity, external potentials, coupling, discontinuity, nonlocality, higher dimensionality, and nonlinear saturation in which Peregrine soliton solutions have been reported.

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