메뉴 건너뛰기




Volumn 59, Issue 6, 1999, Pages 2162-2192

Whitham equations for optical communications: Mathematical theory of NRZ

Author keywords

[No Author keywords available]

Indexed keywords

DATA COMMUNICATION SYSTEMS; ELECTROMAGNETIC DISPERSION; LIGHT MODULATION; NONLINEAR EQUATIONS; WAVE EQUATIONS;

EID: 0033341625     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036139997328155     Document Type: Article
Times cited : (81)

References (44)
  • 1
    • 0000655552 scopus 로고    scopus 로고
    • Topological Landou-Ginzburg theory with a rational potential and the dispersionless KP hierarchy
    • S. AOYAMA AND Y. KODAMA, Topological Landou-Ginzburg theory with a rational potential and the dispersionless KP hierarchy, Comm. Math. Phys., 182 (1996), pp. 185-219.
    • (1996) Comm. Math. Phys. , vol.182 , pp. 185-219
    • Aoyama, S.1    Kodama, Y.2
  • 2
    • 0030568203 scopus 로고    scopus 로고
    • Bit-synchronous polarisation and phase modulation scheme for improving the performance of optical amplifier transmission systems
    • N. S. BERGANO, C. R. DAVIDSON, AND F. HEISMANN, Bit-synchronous polarisation and phase modulation scheme for improving the performance of optical amplifier transmission systems, Electron. Lett., 32 (1996), pp. 52-54.
    • (1996) Electron. Lett. , vol.32 , pp. 52-54
    • Bergano, N.S.1    Davidson, C.R.2    Heismann, F.3
  • 4
    • 33745548390 scopus 로고
    • Self-similar solutions of the Whitham equations and KdV equations with f.-g. boundary conditions,
    • Kiev, V. G. Baryakhov et al., eds., World Scientific, Singapore
    • R. F. BIKBAEV AND V. YU, NOVOKSHENOV, Self-similar solutions of the Whitham equations and KdV equations with f.-g. boundary conditions, in Nonlinear and Turbulent Processes in Physics, Proceedings of the Third International Workshop, Kiev, 1987, Vol. 1, V. G. Baryakhov et al., eds., World Scientific, Singapore, 1988, pp. 32-35.
    • (1987) Nonlinear and Turbulent Processes in Physics, Proceedings of the Third International Workshop , vol.1 , pp. 32-35
    • Bikbaev, R.F.1    Novokshenov, V.Yu.2
  • 5
    • 20444505129 scopus 로고
    • Korteweg-de vries equation with finite-gap boundary conditions, and the whitham deformations of riemann surfaces
    • in Russian
    • R. F. BIKBAEV, Korteweg-de Vries equation with finite-gap boundary conditions, and the Whitham deformations of Riemann surfaces, Funktsional. Anal. i Prilozhen. 23 (1989), pp. 1-10 (in Russian); Funct. Anal. Appl., 23 (1990), pp. 257-266 (English translation).
    • (1989) Funktsional. Anal. I Prilozhen. , vol.23 , pp. 1-10
    • Bikbaev, R.F.1
  • 6
    • 20444505129 scopus 로고
    • English translation
    • R. F. BIKBAEV, Korteweg-de Vries equation with finite-gap boundary conditions, and the Whitham deformations of Riemann surfaces, Funktsional. Anal. i Prilozhen. 23 (1989), pp. 1-10 (in Russian); Funct. Anal. Appl., 23 (1990), pp. 257-266 (English translation).
    • (1990) Funct. Anal. Appl. , vol.23 , pp. 257-266
  • 7
    • 0026907971 scopus 로고
    • Dispersive regularization of the whitham equation for the toda lattice
    • A. M. BLOCH AND Y. KODAMA, Dispersive regularization of the Whitham equation for the Toda lattice, SIAM J. Appl. Math., 52 (1992), pp. 909-928.
    • (1992) SIAM J. Appl. Math. , vol.52 , pp. 909-928
    • Bloch, A.M.1    Kodama, Y.2
  • 8
    • 0012397937 scopus 로고
    • Semiclassical behavior in the NLS equation: Optical shocks-focusing instabilities
    • N. M. Ercolani et al., eds., Plenum, New York
    • J. C. BRONSKI AND D. W. MCLAUGHLIN, Semiclassical behavior in the NLS equation: Optical shocks-focusing instabilities, in Singular Limits of Dispersive Waves, NATO ASI Series B320, N. M. Ercolani et al., eds., Plenum, New York, 1994, pp. 21-38.
    • (1994) Singular Limits of Dispersive Waves, NATO ASI Series , vol.B320 , pp. 21-38
    • Bronski, J.C.1    McLaughlin, D.W.2
  • 9
    • 0003035782 scopus 로고
    • Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamiltonian theory
    • in Russian
    • B. A. DUBROVIN AND S. P. NOVIKOV, Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamiltonian theory, Uspekhi Mat. Nauk, 44 (1989), pp. 29-98 (in Russian); Russian Math. Surveys, 44 (1989), pp. 35 124 (English translation).
    • (1989) Uspekhi Mat. Nauk , vol.44 , pp. 29-98
    • Dubrovin, B.A.1    Novikov, S.P.2
  • 10
    • 0343373091 scopus 로고
    • English translation
    • B. A. DUBROVIN AND S. P. NOVIKOV, Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamiltonian theory, Uspekhi Mat. Nauk, 44 (1989), pp. 29-98 (in Russian); Russian Math. Surveys, 44 (1989), pp. 35 124 (English translation).
    • (1989) Russian Math. Surveys , vol.44 , pp. 35124
  • 11
    • 0039518969 scopus 로고
    • Decay of an initial discontinuity in the defocusing NLS hydrodynamics
    • G. A. EL, V. V. GEOGJAEV A. V. GUREVICH, AND A. L. KRYLOV, Decay of an initial discontinuity in the defocusing NLS hydrodynamics, Phys. D, 87 (1995), pp. 186-192.
    • (1995) Phys. D , vol.87 , pp. 186-192
    • El, G.A.1    Geogjaev, V.V.2    Gurevich, A.V.3    Krylov, A.L.4
  • 12
    • 84980178052 scopus 로고
    • Multiphase averaging and the inverse spectral solution of the korteweg-de vries equation
    • H. FLASCHKA, M. G. FOREST, AND D. W. MCLAUGHLIN, Multiphase averaging and the inverse spectral solution of the Korteweg-de Vries equation, Comm. Pure Appl. Math., 33 (1980), pp. 739-784.
    • (1980) Comm. Pure Appl. Math. , vol.33 , pp. 739-784
    • Flaschka, H.1    Forest, M.G.2    McLaughlin, D.W.3
  • 14
    • 0347468632 scopus 로고    scopus 로고
    • Onset of oscillations in nonsoliton pulses in nonlinear dispersive fibers
    • M. G. FOREST, AND K. T-R. MCLAUGHLIN, Onset of oscillations in nonsoliton pulses in nonlinear dispersive fibers, J. Nonlinear Sci., 7 (1998), pp. 43-62.
    • (1998) J. Nonlinear Sci. , vol.7 , pp. 43-62
    • Forest, M.G.1    McLaughlin, K.T.-R.2
  • 16
    • 0031188710 scopus 로고    scopus 로고
    • Recent progress in dispersion-managed soliton transmission technologies
    • A. HASEGAWA, Y. KODAMA AND A. MARUTA, Recent progress in dispersion-managed soliton transmission technologies, Optical Fiber Tech., 3 (1997), pp. 197-213.
    • (1997) Optical Fiber Tech. , vol.3 , pp. 197-213
    • Hasegawa, A.1    Kodama, Y.2    Maruta, A.3
  • 18
    • 0003154686 scopus 로고
    • Optical solitons in a monomode fibre
    • Y. KODAMA, Optical solitons in a monomode fibre. J. Statist. Phys., 39 (1985), pp. 597-614.
    • (1985) J. Statist. Phys. , vol.39 , pp. 597-614
    • Kodama, Y.1
  • 19
    • 0023345182 scopus 로고
    • Nonlinear pulse propagation in a monomode dielectric guide
    • Y. KODAMA AND A. HASEGAWA, Nonlinear pulse propagation in a monomode dielectric guide, IEEE J. Quantum Electron., 23 (1987), pp. 510-524.
    • (1987) IEEE J. Quantum Electron. , vol.23 , pp. 510-524
    • Kodama, Y.1    Hasegawa, A.2
  • 20
    • 0002255151 scopus 로고
    • Integrability of dispersionless KP hierarchy
    • World Scientific, Singapore
    • Y. KODAMA AND J. GIBBONS, Integrability of dispersionless KP hierarchy, in Proceedings of the Workshop "Nonlinear World," World Scientific, Singapore, 1990, pp. 166-180.
    • (1990) Proceedings of the Workshop "Nonlinear World," , pp. 166-180
    • Kodama, Y.1    Gibbons, J.2
  • 21
    • 0029408936 scopus 로고
    • Analytical theory of guiding center NRZ and RZ signal transmission in normally dispersive nonlinear optical fibers
    • Y. KODAMA AND S. WABNITZ, Analytical theory of guiding center NRZ and RZ signal transmission in normally dispersive nonlinear optical fibers, Optical Lett., 20 (1995), pp. 2291-2293.
    • (1995) Optical Lett. , vol.20 , pp. 2291-2293
    • Kodama, Y.1    Wabnitz, S.2
  • 22
    • 0029370145 scopus 로고
    • Compensation of nrz signal distortion by initial frequency shifting
    • Y. KODAMA AND S. WABNITZ, Compensation of NRZ signal distortion by initial frequency shifting, Electron. Lett., 31 (1995), pp. 1761-1762.
    • (1995) Electron. Lett. , vol.31 , pp. 1761-1762
    • Kodama, Y.1    Wabnitz, S.2
  • 23
    • 0141484222 scopus 로고    scopus 로고
    • Control of nonreturn-to-zero signal distortion by nonlinear gain
    • Y. KODAMA, S. WABNITZ, AND K. TANAKA, Control of nonreturn-to-zero signal distortion by nonlinear gain, Optical Lett., 21 (1996), pp. 719-721.
    • (1996) Optical Lett. , vol.21 , pp. 719-721
    • Kodama, Y.1    Wabnitz, S.2    Tanaka, K.3
  • 24
    • 0002237214 scopus 로고    scopus 로고
    • Minimum channel spacing in wavelength-division-multiplexed nonreturn-to-zero optical fiber transmissions
    • Y. KODAMA, A. MARUTA, AND S. WABNITZ, Minimum channel spacing in wavelength-division-multiplexed nonreturn-to-zero optical fiber transmissions, Optical Lett., 21 (1996), pp. 1815-1817.
    • (1996) Optical Lett. , vol.21 , pp. 1815-1817
    • Kodama, Y.1    Maruta, A.2    Wabnitz, S.3
  • 25
    • 34249975994 scopus 로고
    • Method of averaging for two-dimensional "integrable" equations
    • I. M. KRICHEVER, Method of averaging for two-dimensional "integrable" equations, Funct. Anal. Appl., 22 (1988), pp. 37-52.
    • (1988) Funct. Anal. Appl. , vol.22 , pp. 37-52
    • Krichever, I.M.1
  • 26
    • 84990575581 scopus 로고
    • The small dispersion limit of the Korteweg-de vries equation I, II, III
    • P. D. LAX AND C. D. LEVERMORE, The small dispersion limit of the Korteweg-de Vries equation I, II, III, Comm. Pure Appl. Math., 36 (1983), pp. 253-290; 571-593; 809-829.
    • (1983) Comm. Pure Appl. Math. , vol.36 , pp. 253-290
    • Lax, P.D.1    Levermore, C.D.2
  • 27
    • 84946620339 scopus 로고
    • The hyperbolic nature of the zero dispersion KdV limit
    • C. D. LEVERMORE, The hyperbolic nature of the zero dispersion KdV limit, Comm. Partial Differential Equations, 13 (1988), pp. 495-514.
    • (1988) Comm. Partial Differential Equations , vol.13 , pp. 495-514
    • Levermore, C.D.1
  • 28
    • 0001680501 scopus 로고
    • On the theory of two-dimensional stationary self-focusing of electromagnetic waves
    • in Russian
    • S. V. MANAKOV, On the theory of two-dimensional stationary self-focusing of electromagnetic waves, Pis'ma Zh. Èkspbr. Teoret. Fiz., 65 (1974), pp. 505-516 (in Russian); Soviet Phys. JETP, 38 (1974), pp. 248-253 (English translation).
    • (1974) Pis'ma Zh. Èkspbr. Teoret. Fiz. , vol.65 , pp. 505-516
    • Manakov, S.V.1
  • 29
    • 0000763166 scopus 로고
    • English translation.
    • S. V. MANAKOV, On the theory of two-dimensional stationary self-focusing of electromagnetic waves, Pis'ma Zh. Èkspbr. Teoret. Fiz., 65 (1974), pp. 505-516 (in Russian); Soviet Phys. JETP, 38 (1974), pp. 248-253 (English translation).
    • (1974) Soviet Phys. JETP , vol.38 , pp. 248-253
  • 30
    • 0026124309 scopus 로고
    • Wavelength division multiplexing with solitons in ultra-long distance transmission using lumped amplifiers
    • L. F. MOLLENAUER, S. G. EVANGELIDES, AND J. P. GORDON, Wavelength division multiplexing with solitons in ultra-long distance transmission using lumped amplifiers, J. Lightwave Technol., 9 (1991), pp. 362-367.
    • (1991) J. Lightwave Technol. , vol.9 , pp. 362-367
    • Mollenauer, L.F.1    Evangelides, S.G.2    Gordon, J.P.3
  • 31
    • 0342503505 scopus 로고
    • Birefringent optical fibers: Modulational instability in a near-integrable system
    • A. S. Fokas et al., eds., Springer-Verlag, New York
    • D. J. MURAKI, O. C. WRIGHT, AND D. W. MCLAUGHLIN, Birefringent optical fibers: Modulational instability in a near-integrable system, in Proceedings of the Workshop "Nonlinear Processes in Physics," A. S. Fokas et al., eds., Springer-Verlag, New York, 1993, pp. 242-246.
    • (1993) Proceedings of the Workshop "Nonlinear Processes in Physics," , pp. 242-246
    • Muraki, D.J.1    Wright, O.C.2    McLaughlin, D.W.3
  • 33
    • 0012406658 scopus 로고
    • Nonlinear schrödinger equation and the Bogolyubov-Whitham method of averaging
    • in Russian
    • M. V. PAVLOV, Nonlinear Schrödinger equation and the Bogolyubov-Whitham method of averaging, Teoret. Mat. Fiz., 71 (1987), pp. 351-356 (in Russian); Theoret. Math. Phys., 71 (1987), pp. 584-588 (English translation).
    • (1987) Teoret. Mat. Fiz. , vol.71 , pp. 351-356
    • Pavlov, M.V.1
  • 34
    • 0012406658 scopus 로고
    • 584-588
    • English translation.
    • M. V. PAVLOV, Nonlinear Schrödinger equation and the Bogolyubov-Whitham method of averaging, Teoret. Mat. Fiz., 71 (1987), pp. 351-356 (in Russian); Theoret. Math. Phys., 71 (1987), pp. 584-588 (English translation).
    • (1987) Theoret. Math. Phys. , vol.71
  • 35
    • 0001841091 scopus 로고
    • Soliton equations as dynamical systems on an infinite dimensional Grassman manifold
    • M. SATO, Soliton equations as dynamical systems on an infinite dimensional Grassman manifold, RIMS Kyoto Univ. Kokyuroku, 439 (1981), pp. 30-46.
    • (1981) Rims Kyoto Univ. Kokyuroku , vol.439 , pp. 30-46
    • Sato, M.1
  • 37
    • 84995807081 scopus 로고    scopus 로고
    • 213 Gbit/s (20 × 10.66 Gbit/s), over 9000 km transmission experiment using dispersion slope compensator
    • San Jose, CA, 1998, Postdeadline papers
    • H. TAGA, N. EDAGAWA, M. SUZUKI, N. TAKEDA, K. IMAI, S. YAMAMOTO, AND S. AKIDA, 213 Gbit/s (20 × 10.66 Gbit/s), over 9000 km transmission experiment using dispersion slope compensator, in Proceedings OFC'98, San Jose, CA, 1998, Postdeadline papers, pp. PD13-1-PD13-4.
    • Proceedings OFC'98
    • Taga, H.1    Edagawa, N.2    Suzuki, M.3    Takeda, N.4    Imai, K.5    Yamamoto, S.6    Akida, S.7
  • 38
    • 84990614472 scopus 로고
    • The generation of modulated wavetrains in the solution of the Korteweg-de Vries equation
    • S. VENAKIDES, The generation of modulated wavetrains in the solution of the Korteweg-de Vries equation, Comm. Pure Appl. Math., 38 (1985), pp. 833-909.
    • (1985) Comm. Pure Appl. Math. , vol.38 , pp. 833-909
    • Venakides, S.1
  • 41
    • 0002565931 scopus 로고
    • Modulational instability in a defocussmg coupled nonlinear schrödinger system
    • O. C. WRIGHT, Modulational instability in a defocussmg coupled nonlinear Schrödinger system, Phys. D, 82 (1995), pp. 1-10.
    • (1995) Phys. D , vol.82 , pp. 1-10
    • Wright, O.C.1
  • 43
    • 0000440099 scopus 로고
    • Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media
    • in Russian
    • V. E. ZAKHAROV AND A. B. SHABAT, Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media, Pis'ma Zh. Èksper. Teoret. Fiz., 61 (1971), pp. 118-134 (in Russian); Soviet Phys. JETP, 34 (1972). pp. 62-69 (English translation).
    • (1971) Pis'ma Zh. Èksper. Teoret. Fiz. , vol.61 , pp. 118-134
    • Zakharov, V.E.1    Shabat, A.B.2
  • 44
    • 0009296146 scopus 로고
    • English translation
    • V. E. ZAKHAROV AND A. B. SHABAT, Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media, Pis'ma Zh. Èksper. Teoret. Fiz., 61 (1971), pp. 118-134 (in Russian); Soviet Phys. JETP, 34 (1972). pp. 62-69 (English translation).
    • (1972) Soviet Phys. JETP , vol.34 , pp. 62-69


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.