EDP Sciences logo
Submit your paper
Search
Menu
All issues Volume 29 / No 5 (October 2024) Wuhan Univ. J. Nat. Sci., 29 5 (2024) 430-438 References
Open Access
Issue
Wuhan Univ. J. Nat. Sci.
Volume 29, Number 5, October 2024
Page(s) 430 - 438
DOI https://doi.org/10.1051/wujns/2024295430
Published online 20 November 2024
  1. Chen D Y. Introduction to Solitons[M]. Beijing: Scientific Press, 2006(Ch). [Google Scholar]
  2. Abhinav K, Guha P, Mukherjee I. Study of quasi-integrable and non-holonomic deformation of equations in the NLS and DNLS hierarchy[J]. Journal of Mathematical Physics, 2018, 59(10): 101507. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  3. Hirota R. The Direct Method in Soliton Theory[M]. New York: Cambridge University Press, 2004. [CrossRef] [Google Scholar]
  4. Ma W X, Zhou R G. A coupled AKNS-Kaup-Newell soliton hierarchy[J]. Journal of Mathematical Physics, 1999, 40(9): 4419-4428. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  5. Song Y F, Shi X J, Wu C F, et al. Recent progress of study on optical solitons in fiber lasers[J]. Applied Physics Reviews, 2019, 6(2): 021313. [CrossRef] [PubMed] [Google Scholar]
  6. Mollenauer L, Stolen R, Gordon J. Experimental observations of picosecond pulse narrowing and solitons in optical fibers[J]. IEEE Journal of Quantum Electronics, 1981, 17(12): 2378. [NASA ADS] [CrossRef] [Google Scholar]
  7. Hasegawa A, Tappert F. Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion[J]. Applied Physics Letter, 1973, 23(3): 142-144. [NASA ADS] [CrossRef] [Google Scholar]
  8. Hasegawa A, Tappert F. Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. II. Normal dispersion[J]. Applied Physics Letters, 1973, 23(4): 171-172. [Google Scholar]
  9. Tzoar N, Jain M. Self-phase modulation in long-geometry optical waveguides[J]. Physical Review A, 1981, 23(3): 1266-1270. [NASA ADS] [CrossRef] [Google Scholar]
  10. Lashkin V M. N-soliton solutions and perturbation theory for the derivative nonlinear Schrödinger equation with nonvanishing boundary conditions[J]. Journal of Physics A: Mathematical and Theoretical, 2007, 40(23): 6119-6132. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  11. Anderson D, Lisak M. Nonlinear asymmetric pulse distortion in long optical fibers[J]. Optics Letters, 1982, 7(8): 394. [NASA ADS] [CrossRef] [PubMed] [Google Scholar]
  12. Nakatsuka H, Grischkowsky D, Balant A C. Nonlinear picosecond-pulse propagation through optical fibers with positive group velocity dispersion[J]. Physical Review Letters, 1981, 47(13): 910-913. [NASA ADS] [CrossRef] [Google Scholar]
  13. Lashkin V M. Generation of solitons by a boxlike pulse in the derivative nonlinear Schrödinger equation with nonvanishing boundary conditions[J]. Physical Review E, 2005, 71(6): 066613. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  14. Khalique C M, Plaatjie K, Adeyemo O D. First integrals, solutions and conservation laws of the derivative nonlinear Schrödinger equation[J]. Partial Differential Equations in Applied Mathematics, 2022, 5: 100382. [CrossRef] [Google Scholar]
  15. Chen X J, Lam W K. Inverse scattering transform for the derivative nonlinear Schrödinger equation with nonvanishing boundary conditions[J]. Physical Review E, 2004, 69(6): 066604. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  16. Zhou G Q. Explicit breather-type and pure N-soliton solution of DNLS+ equation with nonvanishing boundary condition[J]. Wuhan University Journal of Natural Sciences, 2013, 18(2): 147-155. [CrossRef] [MathSciNet] [Google Scholar]
  17. Chen X J, Yang J, Lam W K. N-soliton solution for the derivative nonlinear Schrödinger equation with nonvanishing boundary conditions[J]. Journal of Physics A: Mathematical and General, 2006, 39(13): 3263-3274. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  18. Steude l H. The hierarchy of multi-soliton solutions of the derivative nonlinear Schrödinger equation[J]. Journal of Physics A: Mathematical and General, 2003, 36: 1931-1946. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  19. Guo B L, Ling L M, Liu Q P. High-order solutions and generalized Darboux transformations of derivative nonlinear Schrödinger equations[J]. Studies in Applied Mathematics, 2013, 130(4): 317-344. [CrossRef] [MathSciNet] [Google Scholar]
  20. Zakharov V, Shabat A. Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media[J]. Journal of Experimental and Theoretical Physics, 1970, 34:62-69. [NASA ADS] [Google Scholar]
  21. Gagnon L, Stiévenart N. N-soliton interaction in optical fibers: The multiple-pole case[J]. Optics Letters, 1994, 19(9): 619-621. [NASA ADS] [CrossRef] [PubMed] [Google Scholar]
  22. Takahashi M, Konno K. N double pole solution for the modified Korteweg-de Vries equation by the Hirota's method[J]. Journal of the Physical Society of Japan, 1989, 58(10): 3505-3508. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  23. Matveev V B. Positons: Slowly decreasing analogues of solitons[J]. Theoretical and Mathematical Physics, 2002, 131: 483-497. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  24. Zhang Z, Li B, Chen J C, et al. Construction of higher-order smooth positons and breather positons via Hirota's bilinear method[J]. Nonlinear Dynamics, 2021, 105(3): 2611-2618. [NASA ADS] [CrossRef] [Google Scholar]
  25. Liu W, Zhang Y S, He J S. Dynamics of the smooth positons of the complex modified KdV equation[J]. Waves in Random and Complex Media, 2018, 28(2), 203-214. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  26. Xing Q X, Wu Z W, Mihalache D, et al. Smooth positon solutions of the focusing modified Korteweg-de Vries equation[J]. Nonlinear Dynamics, 2017, 89: 2299-2310. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  27. Song W J, Xu S W, Li M H, et al. Generating mechanism and dynamic of the smooth positons for the derivative nonlinear Schrödinger equation[J]. Nonlinear Dynamics, 2019, 97(4): 2135-2145. [NASA ADS] [CrossRef] [Google Scholar]
  28. Zhou H J, Chen Y. High-order soliton solutions and their dynamics in the inhomogeneous variable coefficients Hirota equation[J]. Communications in Nonlinear Science and Numerical Simulation, 2023, 120: 107149. [NASA ADS] [CrossRef] [Google Scholar]
  29. Zhu J Y, Chen Y. A new form of general soliton solutions and multiple zeros solutions for a higher-order Kaup-Newell equation[J]. Journal of Mathematical Physics, 2021, 62(12): 123501. [CrossRef] [Google Scholar]
  30. Peng W Q, Chen Y. Double and triple poles solutions for the Gerdjikov-Ivanov type of derivative nonlinear Schrödinger equations with zero/nonzero boundary conditions[EB/OL]. [2023-10-20]. http://arxiv.org/abs/2104.12073. [Google Scholar]
  31. Kimiaki K, Hiroshi K. Comment on "The novel multi-soliton solutions of the MKdV-sine gordon equation" [J]. Journal of the Physical Society of Japan, 2002, 71(8): 2071. [CrossRef] [Google Scholar]
  32. Chen Z Y, Huang N N. Explicit N-soliton solution of the modified nonlinear Schrödinger equation[J]. Physical Review A, 1990, 41(7): 4066-4069. [NASA ADS] [CrossRef] [PubMed] [Google Scholar]
  33. Tang Y X, Zhou G Q. The rogue wave solution of MNLS/DNLS equation based on Hirota's bilinear derivative transformation[J]. Acta Mathematica Scientia A, 2023, 43: 132-142(Ch). [Google Scholar]
  34. Kaup D J, Newell A C. An exact solution for a derivative nonlinear Schrödinger equation[J]. Journal of Mathematical Physics, 1978, 19(4): 798-801. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  35. Zhou G Q, Huang N. An N-soliton solution to the DNLS equation based on revised inverse scattering transform[J]. Journal of Physics A: Mathematical and Theoretical, 2007, 40: 13607-13623. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  36. Huang N N, Chen Z Y. Alfven solitons[J]. Journal of Physics A: Mathematical and General, 1990, 23(4): 439-453. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  37. Zhou G Q, Bi X T. Soliton solution of the DNLS equation based on Hirota's bilinear derivative transform[J]. Wuhan University Journal of Natural Sciences, 2009, 14(6): 505-510. [CrossRef] [MathSciNet] [Google Scholar]
  38. Li X J, Zhou G Q. Mixed breather-type and pure soliton solution of DNLS equation[J]. Wuhan University Journal of Natural Sciences, 2017, 22(3): 223-232. [CrossRef] [MathSciNet] [Google Scholar]
  39. Zhou G Q, Li X J. Space periodic solutions and rogue wave solution of the derivative nonlinear Schrödinger equation[J]. Wuhan University Journal of Natural Sciences, 2017, 22(5): 373-379. [CrossRef] [MathSciNet] [Google Scholar]
  40. Cai H. Research about MNLS Equation and DNLS Equation[D]. Wuhan: Wuhan University, 2005(Ch). [Google Scholar]
  41. Zhou G Q, Luo R J. Soliton solution of MNLS/DNLS equation with nonvanishing boundary condition based on Hirota method[J]. Phys and Eng, 2023, 33: 79-84(Ch). [Google Scholar]
  42. Wadati M, Ohkuma K. Multiple-pole solutions of the modified Korteweg-de Vries equation[J]. Journal of the Physical Society of Japan, 1982, 51(6): 2029-2035. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  43. Lou S Y, Lin J. Rogue waves in nonintegrable KdV-type systems[J]. Chinese Physics Letters, 2018, 35(5): 050202. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.