Fast sixth-order algorithm based on the generalized Cayley transform for the Zakharov-Shabat system associated with nonlinear Schrodinger equation
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Igor Chekhovskoy | Mikhail Fedoruk | Sergey Medvedev | Irina Vaseva | M. Fedoruk | I. Chekhovskoy | I. Vaseva | S. Medvedev
[1] Vishal Vaibhav. Efficient Nonlinear Fourier Transform Algorithms of Order Four on Equispaced Grid , 2019, IEEE Photonics Technology Letters.
[2] A D Ellis,et al. Timing and phase jitter suppression in coherent soliton transmission. , 2014, Optics letters.
[3] Stefan Kunis,et al. Using NFFT 3---A Software Library for Various Nonequispaced Fast Fourier Transforms , 2009, TOMS.
[4] T. Taha,et al. Analytical and numerical aspects of certain nonlinear evolution equations. II. Numerical, nonlinear Schrödinger equation , 1984 .
[5] W. Magnus. On the exponential solution of differential equations for a linear operator , 1954 .
[6] Jarmo Malinen,et al. The Cayley Transform as a Time Discretization Scheme , 2007 .
[7] Ernst Hairer,et al. Solving Ordinary Differential Equations I: Nonstiff Problems , 2009 .
[8] Sergey I. Vinitsky,et al. A high-order accuracy method for numerical solving of the time-dependent Schrödinger equation , 1999 .
[9] Sander Wahls,et al. Higher Order Exponential Splittings for the Fast Non-Linear Fourier Transform of the Korteweg-De Vries Equation , 2018, 2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).
[10] H. Vincent Poor,et al. Fast Numerical Nonlinear Fourier Transforms , 2014, IEEE Transactions on Information Theory.
[11] S. Blanes,et al. The Magnus expansion and some of its applications , 2008, 0810.5488.
[12] Sergei K. Turitsyn,et al. Nonlinear Fourier Transform for Optical Data Processing and Transmission: Advances and Perspectives , 2017, 2018 European Conference on Optical Communication (ECOC).
[13] Akira Hasegawa,et al. Optical solitons in fibers , 1993, International Commission for Optics.
[14] Evgeniy V. Podivilov,et al. Exactly solvable profiles of quasi-rectangular Bragg filter with dispersion compensation , 2006 .
[15] D. J. Benney,et al. The Propagation of Nonlinear Wave Envelopes , 1967 .
[16] H. Vincent Poor,et al. Introducing the fast nonlinear Fourier transform , 2013, 2013 IEEE International Conference on Acoustics, Speech and Signal Processing.
[17] F. M. Toyama,et al. Accurate numerical solutions of the time-dependent Schrödinger equation. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.
[18] Sander Wahls,et al. Fast Nonlinear Fourier Transform Algorithms Using Higher Order Exponential Integrators , 2019, IEEE Access.
[19] Frank R. Kschischang,et al. Information Transmission Using the Nonlinear Fourier Transform, Part III: Spectrum Modulation , 2013, IEEE Transactions on Information Theory.
[20] E. Hairer,et al. Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems , 2010 .
[21] Sander Wahls,et al. FNFT: A Software Library for Computing Nonlinear Fourier Transforms , 2018, J. Open Source Softw..
[22] Mikhail P. Fedoruk,et al. Conservative multi-exponential scheme for solving the direct Zakharov-Shabat scattering problem. , 2020, Optics letters.
[23] Arieh Iserles,et al. On Cayley-Transform Methods for the Discretization of Lie-Group Equations , 2001, Found. Comput. Math..
[24] Vahid Aref,et al. Time-Bandwidth Product Perspective for Nonlinear Fourier Transform-Based Multi-Eigenvalue Soliton Transmission , 2019, IEEE Transactions on Communications.
[25] Mechthild Thalhammer,et al. High-order commutator-free quasi-Magnus exponential integrators for non-autonomous linear evolution equations , 2017, Comput. Phys. Commun..
[26] Luciano Lopez,et al. The Cayley transform in the numerical solution of unitary differential systems , 1998, Adv. Comput. Math..
[27] Vladimir E. Zakharov,et al. Stability of periodic waves of finite amplitude on the surface of a deep fluid , 1968 .
[28] Akira Hasegawa,et al. Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion , 1973 .
[29] S. Blanes,et al. Fourth-and sixth-order commutator-free Magnus integrators for linear and non-linear dynamical systems , 2006 .
[30] A. Hasegawa,et al. Eigenvalue communication , 1993 .
[31] J. L. Blue,et al. Rational approximations to matrix exponential for systems of stiff differential equations , 1970 .
[32] Holger Fehske,et al. High-order commutator-free exponential time-propagation of driven quantum systems , 2011, J. Comput. Phys..
[33] Sergei K. Turitsyn,et al. Physics and mathematics of dispersion-managed optical solitons , 2003 .
[34] Francesco Da Ros,et al. Dual polarization nonlinear Fourier transform-based optical communication system , 2018, ArXiv.
[35] Irina Vaseva,et al. Introducing phase jump tracking - a fast method for eigenvalue evaluation of the direct Zakharov-Shabat problem , 2020, ArXiv.
[36] Morteza Kamalian Kopae,et al. Analysis of laser radiation using the Nonlinear Fourier transform , 2019, Nature Communications.
[37] A. Iserles,et al. Lie-group methods , 2000, Acta Numerica.
[38] B. Fornberg. Generation of finite difference formulas on arbitrarily spaced grids , 1988 .
[39] Cleve B. Moler,et al. Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later , 1978, SIAM Rev..
[40] Mansoor I. Yousefi,et al. Multieigenvalue Communication , 2016, Journal of Lightwave Technology.
[41] A. Zvezdin,et al. Contribution to the nonlinear theory of magnetostatic spin waves , 2008 .
[42] V. Zakharov,et al. Exact Theory of Two-dimensional Self-focusing and One-dimensional Self-modulation of Waves in Nonlinear Media , 1970 .
[43] Sergey Medvedev,et al. Exponential Fourth Order Schemes for Direct Zakharov-Shabat problem , 2019, Optics express.
[44] A. Osborne,et al. Computation of the direct scattering transform for the nonlinear Schroedinger equation , 1992 .
[45] S. Burtsev,et al. Numerical Algorithms for the Direct Spectral Transform with Applications to Nonlinear Schrödinger Type Systems , 1998 .
[46] R. S. Varga,et al. On the zeros and poles of Padé approximants toez. III , 1978 .
[47] A. Vasylchenkova,et al. Direct nonlinear Fourier transform algorithms for the computation of solitonic spectra in focusing nonlinear Schrödinger equation , 2017, Commun. Nonlinear Sci. Numer. Simul..
[48] S. Turitsyn,et al. Polarization-multiplexed nonlinear inverse synthesis with standard and reduced-complexity NFT processing. , 2018, Optics express.
[49] D. Calahan. Numerical solution of linear systems with widely separated time constants , 1967 .
[50] F. Kschischang,et al. Bi-Directional Algorithm for Computing Discrete Spectral Amplitudes in the NFT , 2016, Journal of Lightwave Technology.
[51] S. Turitsyn,et al. Nonlinear Fourier Transform for Analysis of Coherent Structures in Dissipative Systems. , 2019, Physical review letters.
[52] V. Zakharov. Collapse of Langmuir Waves , 1972 .
[53] Francesco Da Ros,et al. Dual-Polarization NFDM Transmission With Continuous and Discrete Spectral Modulation , 2019, Journal of Lightwave Technology.