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Stationary Solutions for Nonlinear Schrödinger Equations by Lie Group Analysis

S.T. Raza Rizvi, I. Afzal, K. Ali, M. Younis
2019 Acta Physica Polonica. A  
In this paper we obtain the stationary solutions of various nonlinear Schrödinger equations.  ...  We use Lie symmetry method to find the stationary solutions of the Gerdjikov-Ivanov equation, cubic-quintic and paraxial nonlinear Schrödinger equations.  ...  Zhang et al. studied the interactions of vector antidark solitons for the coupled nonlinear Schrödinger equation in inhomogeneous fibers [19] .  ... 
doi:10.12693/aphyspola.136.187 fatcat:3isgo66sqfhslk7j34iuualvne

Controllable Kuznetsov Ma-like breather generation via dispersion modulation in the nonlinear Schrödinger equation with variable coefficients [article]

Dipti Kanika Mahato, Amarendra K. Sarma
2021 arXiv   pre-print
The nonlinear Schrödinger equation with variable coefficients has applications in numerous areas of physics,specifically in the context of nonlinear optics and Bose-Einstein condensate.  ...  In this work, we have studied various orders of rational solution of the variable coefficient nonlinear Schrödinger equation.  ...  The nonlinear Schrödinger equation with variable coefficients has applications in numerous areas of physics,specifically in the context of nonlinear optics and Bose-Einstein condensate.  ... 
arXiv:1910.00936v2 fatcat:f2ibpsfwungkjkyvfls72rkpfm

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

T. Uthayakumar, L. Al Sakkaf, U. Al Khawaja
2020 Frontiers in Physics  
, higher dimensionality, and nonlinear saturation in which Peregrine soliton solutions have been reported.  ...  Subsequently, we collect all forms of nonlinear Schrödinger equations, involving systematically the effects of higher-order nonlinearity, inhomogeneity, external potentials, coupling, discontinuity, nonlocality  ...  ACKNOWLEDGMENTS The authors acknowledge the support of UAE University through grants UAEU-UPAR(1) 2019 and UAEU-UPAR(11) 2019.  ... 
doi:10.3389/fphy.2020.596886 fatcat:3ec4qdghdzb4vg3nrobmkdvxwy

Generalized solitary waves in nonintegrable KdV equations

Tadas Telksnys, Zenonas Navickas, Minvydas Ragulskis, Romas Marcinkevicius
2016 Journal of Vibroengineering  
Computational experiments illustrate the variety of new solitary solutions and their generating equations.  ...  The generalization of the classical Korteweg-de-Vries (KdV) solitary wave solution is presented in this paper. The amplitude and the propagation speed of generalized KdV solitary waves vary in time.  ...  MIP078/15 from the Research Council of Lithuania.  ... 
doi:10.21595/jve.2016.16941 fatcat:5w6ox3dnxvcixm7maayhls6gti

Manipulation of vector solitons in a system of inhomogeneous coherently coupled nonlinear Schrödinger models with variable nonlinearities

R Babu Mareeswaran, Karuppaiya Sakkaravarthi, T Kanna
2020 Journal of Physics A: Mathematical and Theoretical  
This general CCNLS system encompasses three distinct types of CCNLS equations that describe the dynamics of beam propagation in an inhomogeneous Kerr-like nonlinear optical medium for different choices  ...  With the help of a non-standard Hirota's bilinearization method and exact soliton solutions, we explore the impact of varying nonlinearities and refractive index in the propagation and collisions analytically  ...  Acknowledgment The work KS was supported by Department of Science and Technology -Science and Engineering  ... 
doi:10.1088/1751-8121/abae3f fatcat:6iboandk7vberklgl3xp7q73hi

Solitary waves in the nonlinear Schrödinger equation with Hermite-Gaussian modulation of the local nonlinearity

Wei-Ping Zhong, Milivoj R. Belić, Boris A. Malomed, TingWen Huang
2011 Physical Review E  
We demonstrate "hidden solvability" of the nonlinear Schrödinger (NLS) equation whose nonlinearity coefficient is spatially modulated by Hermite-Gaussian functions of different order and the external potential  ...  The stability of these solutions is verified by means of direct integration of the underlying NLS equation.  ...  8 special solutions was verified by means of direct integration of the full underlying equation.  ... 
doi:10.1103/physreve.84.046611 pmid:22181300 fatcat:oum2siklhrbfvdmnjt4nfahlhq

Soliton models in resonant and nonresonant optical fibers

K Porsezian
2001 Pramana (Bangalore)  
birefringence, self-induced transparency and various inhomogeneous effects in fibers, the completely integrable concept and bright, dark and self-induced transparency soliton models in nonlinear fiber  ...  In this review, considering the important linear and nonlinear optical effects like group velocity dispersion, higher order dispersion, Kerr nonlinearity, self-steepening, stimulated Raman scattering,  ...  Acknowledgements The author wishes to thank DST and NBHM, Government of India, for financial support through research projects.  ... 
doi:10.1007/s12043-001-0012-1 fatcat:4icfjis5vve3longfrstuyimya

Vector solitons in coupled nonlinear Schrödinger equations with spatial stimulated scattering and inhomogeneous dispersion [article]

E. M. Gromov, B. A. Malomed, V. V. Tyutin
2017 arXiv   pre-print
The dynamics of two-component solitons is studied, analytically and numerically, in the framework of a system of coupled extended nonlinear Schr\"odinger equations, which incorporate the cross-phase modulation  ...  The corresponding approximate analytical solutions for stable solitons are found. Analytical results are well confirmed by their numerical counterparts.  ...  Soliton solutions are considered in many models of nonlinear propagation of wave fields in dispersive media, which occur in various areas of physics: optical pulses in fibers, electromagnetic waves in  ... 
arXiv:1705.06722v1 fatcat:2kzmrus6vbhxlnleiqzzfh6moe

Characterization and Application of Solitons in a High Nonlinearity Optical Link with Dense Wavelength Division Multiplexing (DWDM) and Ultra-Dense Wavelength Division Multiplexing (UDWDM) Technics

Aristide Mankiti Fati, Rostand Davy Martialy Loembe Souamy, Fraidy Ghislain Bouesse, . Nzonzolo, André Pasi Bengi Massata, Camille Nziengui Mabika, Badila Nkodia Chilperic
2021 Journal of Engineering Research and Reports  
In this article, we are presenting the use of optical solitons in the fiber optic link, with a particular way; we have considered two kind of links, the underground one and the overhead one, in the first  ...  link, we have applied optical soliton in order to just take into account the optical Kerr effect.  ...  the technical director of Congo telecom for providing partial support for carrying out this research work.  ... 
doi:10.9734/jerr/2021/v20i917378 fatcat:6a35vogzsvb3xhdxfyoomatyny

Roadmap on optical rogue waves and extreme events

Nail Akhmediev, Bertrand Kibler, Fabio Baronio, Milivoj Belić, Wei-Ping Zhong, Yiqi Zhang, Wonkeun Chang, Jose M Soto-Crespo, Peter Vouzas, Philippe Grelu, Caroline Lecaplain, K Hammani (+26 others)
2016 Journal of Optics  
After all, rogue waves may appear for a multiplicity of reasons and not necessarily only in optical fibers and not only in the process of supercontinuum generation.  ...  We know by now that rogue waves may be generated by lasers, appear in wide aperture cavities, in plasmas and in a variety of other optical systems.  ...  Acknowledgments and funding information Acknowledgments and funding information This work has been supported in part by the Spanish MINECO (FIS2015-66503-C3-2-P) and ICREA ACADEMIA.  ... 
doi:10.1088/2040-8978/18/6/063001 fatcat:fz3zxhx5yve5zck2pbhy6zye3i

Optical rogue waves in the generalized inhomogeneous higher-order nonlinear Schrödinger equation with modulating coefficients

Zhenya Yan, Chaoqing Dai
2013 Journal of Optics  
We consider optical rogue wave solutions and interactions for the generalized higher-order nonlinear Schrödinger (NLS) equation with space- and time-modulated parameters.  ...  A proper transformation is presented to reduce the generalized higher-order NLS equation to the integrable Hirota equation with constant coefficients.  ...  ACKNOWLEDGMENTS The work was supported by the NSFC under Grant Nos. 11071242, 61178091, and 11005092, and the Zhe-jiang Provincial Natural Science Foundation of China under Grant No. Y13F050037.  ... 
doi:10.1088/2040-8978/15/6/064012 fatcat:5xn4fjvfurbudhh3ee4v3fvdem

Wide vector solitons in systems with time- and space-modulated nonlinearities

L. E. Arroyo Meza, A. de Souza Dutra, M. B. Hott
2013 Physical Review E  
The method applied here allows us to find a class of wide localized (in space) vector soliton solutions of nonautonomous nonlinear Schrödinger equations.  ...  The vector solitons found here can be applied to theoretical studies of Bose-condensed atoms in two different internal states and of ultrashort pulse propagation in optical fibers with focusing and defocusing  ...  in order to reach two coupled nonlinear second-order differential equations with homogeneous coefficients.  ... 
doi:10.1103/physreve.88.053202 pmid:24329370 fatcat:w4ep4ipourayfnpbv6mnodmqju

Mathematical Modeling of Rogue Waves: A Survey of Recent and Emerging Mathematical Methods and Solutions

Sergio Manzetti
2018 Axioms  
The standard nonlinear Schrödinger equation, the Hirota equation, the MMT equation and further to other models are discussed, and their properties highlighted.  ...  In this survey, a comprehensive perspective of the most recent developments in methods for representing rogue waves is given, along with discussion of the devised and forms and solutions.  ...  The "self-similar" solution found in the process 116 of the transformation of the variable coefficient inhomogenous nonlinear Schrödinger equation into 117 the standard nonlinear Schrödinger equation can  ... 
doi:10.3390/axioms7020042 fatcat:amnl5wub2vbyjbhxwwhit62ypu

Spatially modulated two- and three- component Rabi-coupled Gross-Pitaevskii systems

T Kanna, A Annamalar Sheela, R Babu Mareeswaran
2019 Journal of Physics A: Mathematical and Theoretical  
For this purpose, we obtain the RW solution of the two- and three-component inhomogeneous Gross-Pitaevskii (GP) systems with Rabi coupling by introducing suitable rotational and similarity transformations  ...  Then, we investigate the effect of inhomogeneity (spatially varying dispersion, trapping potential and nonlinearity) on vector RWs for two different forms of potential strengths, namely periodic (optical  ...  K is supported by Science and Engineering Research Board, Department of Science and Technology (DST-SERB), Government of India, in the form of a major research project (File No.EMR/2015/ 001408). A.  ... 
doi:10.1088/1751-8121/ab330d fatcat:lqfrlvlmxnh6bcvptwntjxqm4q

Propagating Wave Patterns in a Derivative Nonlinear Schrödinger System with Quintic Nonlinearity [article]

C. Rogers Australian Research Council Centre of Excellence for Mathematics & Statistics of Complex Systems, School of Mathematics, The University of New South Wales, Australia, Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Israel, Department of Mechanical Engineering, University of Hong Kong, Hong Kong)
2012 arXiv   pre-print
Exact expressions are obtained for a diversity of propagating patterns for a derivative nonlinear Schr\"odinger equation with a quintic nonlinearity.  ...  The derivative quintic nonlinear Schr\"odinger model equations investigated here are important in the analysis of strong optical signals propagating in spatial or temporal waveguides.  ...  in the analysis of the propagation of temporal pulses along fibers. 6, 7) The one dimensional NLS equation which includes only dispersion and cubic nonlinearity is exactly integrable. 1) Higher order  ... 
arXiv:1207.2561v1 fatcat:r2h6ibvesvdupf3lndcw24qahq
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