Algorithms for solving scattering problems for the Manakov model of nonlinear Schrödinger equations

References

[1] M. J. Ablowitz and H. Segur, Solitons and the Inverse Scattering Transform, SIAM Stud. Appl. Math. 4, Society for Industrial and Applied Mathematics, Philadelphia, 1981. 10.1137/1.9781611970883Suche in Google Scholar

[2] V. Aref, S. T. Le and H. Buelow, Modulation over nonlinear fourier spectrum: Continuous and discrete spectrum, IEEE J. Lightwave Technol. 36 (2018), 1289–1295. 10.1109/JLT.2018.2794475Suche in Google Scholar

[3] A. M. Basharov and A. I. Maimistov, Self-induced transparency when the resonance energy levels are degenerate, Sov. Phys. JETP 60 (1984), 913–919. Suche in Google Scholar

[4] O. V. Belai, L. L. Frumin, E. V. Podivilov and D. A. Shapiro, Efficient numerical method of the fiber Bragg grating synthesis, J. Opt. Soc. Amer. B Opt. Phys. 24 (2007), no. 7, 1451–1457. 10.1364/JOSAB.24.001451Suche in Google Scholar

[5] O. V. Belai, L. L. Frumin, E. V. Podivilov and D. A. Shapiro, Inverse scattering for the one-dimensional Helmholtz equation: Fast numerical method, Opt. Lett. 33 (2008), 2101–2103. 10.1364/OL.33.002101Suche in Google Scholar

[6] O. V. Belai, L. L. Frumin, E. V. Podivilov and D. A. Shapiro, Inverse scattering problem for gratings with deep modulation, Laser Phys. 20 (2010), 318–324. 10.1134/S1054660X10030023Suche in Google Scholar

[7] D. S. Bernstein, Matrix Mathematics. Theory, Facts, and Formulas with Application to Linear Systems Theory, Princeton University, Princeton, 2005. Suche in Google Scholar

[8] R. E. Blahut, Fast Algorithms for Digital Signal Processing, Addison-Wesley, Reading, 1985. 10.1007/978-94-009-5113-6_8Suche in Google Scholar

[9] A. Buryak, J. Bland-Hawthorn and V. Steblina, Comparison of inverse scattering algorithms for designing ultrabroadband fibre Bragg gratings, Opt. Express 17 (2009), 1995–2004. 10.1364/OE.17.001995Suche in Google Scholar

[10] L. L. Frumin, O. V. Belai, E. V. Podivilov and D. A. Shapiro, Efficient numerical method for solving the direct Zakharov–Shabat scattering problem, J. Opt. Soc. Am. B 32 (2015), 290–296. 10.1364/JOSAB.32.000290Suche in Google Scholar

[11] L. L. Frumin, A. A. Gelash and S. K. Turitsyn, New approaches to coding information using inverse scattering transform, Phys. Rev. Lett. 118 (2017), no. 22, Article ID 223901. 10.1103/PhysRevLett.118.223901Suche in Google Scholar PubMed

[12] F. R. Gantmacher, The Theory of Matrices, AMS Chelsea, Providence, 2000. Suche in Google Scholar

[13] R. Hirota, Exact solution of the Korteweg–de Vries equation for multiple collisions of solitons, Phys. Rev. Lett. 27 (1971), 1192–1194. 10.1103/PhysRevLett.27.1192Suche in Google Scholar

[14] T. Kanna and M. Lakshmanan, Exact soliton solutions of coupled nonlinear Schroedinger equations: Shape–changing collisions, logic gates, and partially coherent solitons, Phys. Rev. E 67 (2003), Article ID 046617. 10.1103/PhysRevE.67.046617Suche in Google Scholar

[15] Y. S. Kivshar and G. Agrawal, Optical Solitons: From Fibers to Photonic Crystals, Academic Press, New York, 2003. 10.1016/B978-012410590-4/50012-7Suche in Google Scholar

[16] G. L. Lamb, Jr., Elements of Soliton Theory, John Wiley & Sons, New York, 1980. Suche in Google Scholar

[17] S. Le, J. Prilepskiy and S. Turitsyn, Nonlinear inverse synthesis for high spectral efficiency transmission in optical fibers, Opt. Express 22 (2014), 26720–26741. 10.1364/OE.22.026720Suche in Google Scholar

[18] N. Levinson, The Wiener RMS (root mean square) error criterion in filter design and prediction, J. Math. Phys. Mass. Inst. Tech. 25 (1947), 261–278. 10.1007/978-1-4612-5335-8_16Suche in Google Scholar

[19] A. I. Maimistov, Solitons in nonlinear optics, Sov. J. Quantum Electron. 40 (2010), 756–781. 10.1070/QE2010v040n09ABEH014396Suche in Google Scholar

[20] A. I. Maimistov and A. M. Basharov, Nonlinear Optical Waves, Kluwer Academic, Dordrecht, 1999. 10.1007/978-94-017-2448-7Suche in Google Scholar

[21] A. I. Maimistov and A. M. Basharov, Nonlinear Optical Waves, Springer, Cham, 2013. Suche in Google Scholar

[22] A. I. Maimistov, A. M. Basharov, S. O. Elyutin and Y. M. Sklyarov, Present state of self-induced transparency theory, Phys. Rep. 191 (1990), 1–108. 10.1016/0370-1573(90)90142-OSuche in Google Scholar

[23] S. V. Manakov, On the theory of two-dimensional stationary self-focusing of electromagnetic waves, Sov. Phys. JETP 38 (1974), 248–253. Suche in Google Scholar

[24] L. F. Mollenauer and J. P. Gordon, Solitons in Optical Fibers: Fundamentals and Applications, Academic Press, New York, 2006. Suche in Google Scholar

[25] S. Olver, A general framework for solving Riemann–Hilbert problems numerically, Numer. Math. 122 (2012), no. 2, 305–340. 10.1007/s00211-012-0459-7Suche in Google Scholar

[26] R. Radhakrishnan, M. Lakshmanan and J. Hietarinta, Inelastic collision and switching of coupled bright solitons in optical fibers, Phys. Rev. E 56 (1997), 2213–2216. 10.1103/PhysRevE.56.2213Suche in Google Scholar

[27] C. Rogers and W. F. Shadwick, Bäcklund Transformations and Their Applications, Math. Sci. Eng. 161, Academic Press, New York, 1982. Suche in Google Scholar

[28] S. K. Turitsyn, J. E. Prilepsky, S. T. Le, S. Wahls, L. L. Frumin, M. Kamalian and S. A. Derevyanko, Nonlinear Fourier transform for optical data processing and transmission: Advances and perspectives, Optica 4 (2017), 307–322. 10.1109/ECOC.2018.8535515Suche in Google Scholar

[29] V. E. Zaharov, S. V. Manakov, S. P. Novikov and L. P. Pitaevskiĭ, Theory of Solitons: The Inverse Scattering Method, Springer, Cham, 1984. Suche in Google Scholar

[30] V. E. Zakharov and A. V. Mikhaĭlov, Relativistically invariant two-dimensional models of field theory which are integrable by means of the inverse scattering problem method, Sov. Phys. JETP 47 (1978), 1017–1027. Suche in Google Scholar

[31] V. E. Zakharov and A. B. Shabat, Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media, Ž. Èksper. Teoret. Fiz. 61 (1971), no. 1, 118–134. Suche in Google Scholar