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Information Transmission Using the Nonlinear Fourier Transform, Part II: Numerical Methods

Mansoor I. Yousefi, Frank R. Kschischang
2014 IEEE Transactions on Information Theory  
These methods are used to compute the spectrum of various signals commonly used in the optical fiber communications.  ...  In this paper, numerical methods are suggested to compute the discrete and the continuous spectrum of a signal with respect to the Zakharov-Shabat system, a Lax operator underlying numerous integrable  ...  Nonlinear Fourier Transform of Pulses in Data Communications In this section, we use the numerical methods discussed in Section 5.1 to compute the nonlinear Fourier transform of signals typically used  ... 
doi:10.1109/tit.2014.2321151 fatcat:pbphf7fyknb37mcgzz5ppsmbhi

Information Transmission Using the Nonlinear Fourier Transform, Part I: Mathematical Tools

Mansoor I Yousefi, Frank R Kschischang
2014 IEEE Transactions on Information Theory  
In this transmission scheme, which can be viewed as a nonlinear analogue of orthogonal frequency-division multiplexing commonly used in linear channels, information is encoded in the nonlinear frequencies  ...  The nonlinear Fourier transform (NFT), a powerful tool in soliton theory and exactly solvable models, is a method for solving integrable partial differential equations governing wave propagation in certain  ...  In [Part II] numerical methods are suggested to compute the nonlinear Fourier transform of a signal with respect to the AKNS Lax operator.  ... 
doi:10.1109/tit.2014.2321143 fatcat:igqhmurhvfaannb3x6rxmj7icu

Information Transmission Using the Nonlinear Fourier Transform, Part III: Spectrum Modulation

Mansoor I. Yousefi, Frank R. Kschischang
2014 IEEE Transactions on Information Theory  
However, this distortion and similar ones arising from nonlinearity are primarily due to the use of methods suited for linear systems, namely WDM and linear pulse-train transmission, for the nonlinear  ...  In this paper, emphasis is placed on modulation of the discrete component of the nonlinear Fourier transform of the signal and some simple examples of achievable spectral efficiencies are provided.  ...  INTRODUCTION T HIS PAPER is a continuation of Part I [1] and Part II [2] on data transmission using the nonlinear Fourier transform (NFT).  ... 
doi:10.1109/tit.2014.2321155 fatcat:wnyrhcro4vfyvascdvlikbksku

Numerical methods for the inverse nonlinear fourier transform

Stella Civelli, Luigi Barletti, Marco Secondini
2015 2015 Tyrrhenian International Workshop on Digital Communications (TIWDC)  
We introduce a new numerical method for the computation of the inverse nonlinear Fourier transform and compare its computational complexity and accuracy to those of other methods available in the literature  ...  For a given accuracy, the proposed method requires the lowest number of operations  ...  CONCLUSIONS A new numerical method for the computation of the inverse nonlinear Fourier transform has been proposed.  ... 
doi:10.1109/tiwdc.2015.7323325 dblp:conf/tiwdc/CivelliBS15 fatcat:dkua4bh5rfcfvaq36wldwgatxu

Conservative numerical methods for nonlinear strings

Stefan Bilbao
2005 Journal of the Acoustical Society of America  
be arrived at without any reliance on frequency domain concepts ͑i.e., Fourier or Laplace transforms͒, which are of only moderate utility in the analysis of nonlinear systems.  ...  In this article, a class of numerical schemes for the simulation of nonlinear coupled longitudinal/ transverse string vibration is presented.  ...  Am., Vol. 118, No. 5, November 2005 Stefan Bilbao: Conservative numerical methods for nonlinear strings  ... 
doi:10.1121/1.2046787 fatcat:7vnj65a56zb6xnwij2xxm4ekay

A numerical method for computing radially symmetric solutions of a dissipative nonlinear modified Klein-Gordon equation

J. E. Macías-Díaz, A. Puri
2005 Numerical Methods for Partial Differential Equations  
Part of our study will be devoted to compare the physical effects of the damping coefficients.  ...  internal and external damping coefficients are constant, and the nonlinear term follows a power law.  ...  The use of the discrete Fourier transform is a useful tool in the analysis of stability of finite-difference schemes for initial-value problems.  ... 
doi:10.1002/num.20094 fatcat:f2f7ehzdh5dw5kgjceixb2ubue

The Gaussian semiclassical soliton ensemble and numerical methods for the focusing nonlinear Schrödinger equation [article]

Long Lee, Gregory Lyng, Irena Vankova
2012 arXiv   pre-print
a numerical implementation of the inverse scattering transform for a special case in which the scattering data is known exactly.  ...  We report on a number of careful numerical experiments motivated by the semiclassical (zero-dispersion, \epsilon\downarrow 0) limit of the focusing nonlinear Schr\"odinger equation.  ...  (A) Nonlinear part (solve exactly in physical space) part (solve exactly in Fourier space): ( 3 .Step 3 :. 1 . 331 17) Solving the ODE (3.15) with the initial time t n + 1 4 ∆t and the final time t n  ... 
arXiv:1207.0824v1 fatcat:i46themajngcbkvtqsmvei5luy

Advances in numerical methods [chapter]

2010 Computational Modelling of Concrete Structures  
Public reporting bindsn for this collection ot information ii estimated to average 1 hour per response, including the time for reviewing instruction!  ...  , searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information.  ...  Acknowledgements We would like to thank Ru-Shan Wu for stimulating discussions which led to the F-K analysis of phase planes.  ... 
doi:10.1201/b10546-31 fatcat:exlb6ij4zjh5ff7xqtl7wt6geq

Analyzing Data [chapter]

George Lindfield, John Penny
2019 Numerical Methods  
. , ' With the aid of the Inverse Fourier transform, % Combinini Equations (2.40) and (2.44) , % ,f.  ...  (3.41) %1 then the square root matrix 0 may' be updated in time using Potter'na fnotor~sation of (3.38). Thinl method was . • •.••gliven before as part of Method No.  ...  This 'coordinate transformation matrix is, then used to transform the accelerometer outputs from the body eases to the computing axes.  ... 
doi:10.1016/b978-0-12-812256-3.00016-6 fatcat:iwfrlexsajeb5pitrqy6nuqzqy

The Mollification Method and the Numerical Solution of Ill-Posed Problems (Diego A. Murio)

James V. Beck
1994 SIAM Review  
of transmissivity coefficients in linear and nonlinear elliptic and parabolic equations in one space dimension.  ...  Numerical Method, 194 6.11.  ... 
doi:10.1137/1036117 fatcat:3b5wuk3xivczvmjmycch4g2r5i

Data Transmission based on Exact Inverse Periodic Nonlinear Fourier Transform, Part II: Waveform Design and Experiment [article]

Jan-Willem Goossens, Hartmut Hafermann, Yves Jaouën
2019 arXiv   pre-print
The nonlinear Fourier transform has the potential to overcome limits on performance and achievable data rates which arise in modern optical fiber communication systems when nonlinear interference is treated  ...  The periodic nonlinear Fourier transform (PNFT) has been much less investigated compared to its counterpart based on vanishing boundary conditions.  ...  VII concludes the paper. II. Periodic nonlinear Fourier transform The periodic nonlinear Fourier transform hinges on the applicability of an integrable model for light propagation in optical fiber.  ... 
arXiv:1911.12615v1 fatcat:xuabmsme5nbtzduui67qfhtg34

The Gaussian semiclassical soliton ensemble and numerical methods for the focusing nonlinear Schrödinger equation

Long Lee, Gregory Lyng, Irena Vankova
2012 Physica D : Non-linear phenomena  
a numerical implementation of the inverse scattering transform for a special case in which the scattering data is known exactly.  ...  We report on a number of careful numerical experiments motivated by the semiclassical (zerodispersion, ↓ 0) limit of the focusing nonlinear Schrödinger equation.  ...  The authors would like to thank Ken McLaughlin, Peter Miller, and Jared Bronski for useful conversations about the semiclassical limit of the focusing NLS equation.  ... 
doi:10.1016/j.physd.2012.08.006 fatcat:7fus4cv2nfd4lischatex65xyu

Dynamics of structures coupled with elastic media—A review of numerical models and methods

D. Clouteau, R. Cottereau, G. Lombaert
2013 Journal of Sound and Vibration  
The general setting for a linear bounded structure coupled to an unbounded linear environment through a bounded interface is first recalled, and the domain decomposition technique classically used for  ...  Finally, the ongoing research in the fields of unbounded interface, moving interface, and multiple interfaces are reviewed and summarized.  ...  Both can be easily computed using either the reflection-transmission techniques [130] or the stiffness matrix method [131] .  ... 
doi:10.1016/j.jsv.2012.10.011 fatcat:q7sl2nuiqjdondtfk76n6gtnji

Contribution to the study of efficient iterative methods for the numerical solution of partial differential equations [article]

Vasseur Xavier
2016 Zenodo  
of the Habilitation manuscript: Multigrid and domain decomposition methods provide efficient algorithms for the numerical solution of partial differential equations arising in the modelling of many applications  ...  The efficiency of the numerical methods is demonstrated on challenging applications in seismics requiring the solution of huge linear systems of equations with multiple right-hand sides on parallel distributed  ...  ACKNOWLEDGEMENTS The authors would like to thank the two referees for their valuable comments and suggestions that helped us to improve the manuscript. They thank Prof. A. Borzi and Prof. C. W.  ... 
doi:10.5281/zenodo.5813538 fatcat:jhsbgwinxngcpe53ewid6ygo7i

Spectral Finite-Element Methods for Parametric Constrained Optimization Problems

Mihai Anitescu
2009 SIAM Journal on Numerical Analysis  
Numerical results in one-dimensional cases indicate that our method is, for those examples, superior in both accuracy and speed to blackbox approaches.  ...  We present a method to approximate the solution mapping of parametric constrained optimization problems.  ...  Mihai Anitescu was supported by the Mathematical, Information, and Computational Sciences Division subprogram of the Office of Advanced Scientific Computing Research, Office of Science, U.S.  ... 
doi:10.1137/060676374 fatcat:zljgqc2yqjcgvmhwroqjr2ym74
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