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(2 + 1) dimensional Hărăgus-Courcelle-Il’ichev model for the liquid surface waves in the presence of sea ice or surface tension: Bäcklund transformation, exact solutions and possibly observable effects

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Abstract.

The wave propagation on an ocean or water surface in the presence of sea ice or surface tension is of current importance. In this paper, we investigate the (2 + 1) dimensional 6th-order model proposed recently by Hărăgus-Courcelle and Il’ichev for such wave propagation. Firstly, we correct some errors in the original derivations of this model. With computerized symbolic computation and truncated Painlevé expansion, we then obtain an auto-Bäcklund transformation and types of the solitonic and other exact analytic solutions to the model, with the solitary waves as a special case, able to be dealt with the powerful Wu method. Based on the results, we later propose some possibly observable effects for the future experiments, and in the end, provide a possible way to explain the regular structure of the open-sea ice break-up observations.

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References

  1. A. Müller, B. Ettema, Proc. IAHR Ice Symp., Hamburg, II, 287 (1992)

  2. V. Squire, Cold Reg. Sci. Tech. 10, 59 (1984)

    Google Scholar 

  3. L. Forbes, J. Fluid Mech. 169, 409 (1986)

    MATH  MathSciNet  ADS  Google Scholar 

  4. L. Forbes, J. Fluid Mech. 188, 491 (1988)

    MATH  MathSciNet  ADS  Google Scholar 

  5. M. Hărăgus-Courcelle, A. Il’ichev, Eur. J. Mech. B 17, 739 (1998)

    MATH  Google Scholar 

  6. A. Il’ichev, Eur. J. Mech. B 18, 501 (1999)

    MATH  MathSciNet  Google Scholar 

  7. A. Il’ichev, Fluid Dynamics 35, 157 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  8. I. Bakholdin, A. Il’ichev, Eur. J. Mech. B 22, 291 (2003)

    MATH  MathSciNet  Google Scholar 

  9. T. Benjamin, Q. Appl. Math. 40, 231 (1982)

    MATH  MathSciNet  Google Scholar 

  10. G. Iooss, K. Kirchgässner, C.R. Acad. Sci. Paris 311, 265 (1990)

    MATH  MathSciNet  Google Scholar 

  11. G. Iooss, K. Kirchgässner, Proc. Roy. Soc. Edinburgh A 122, 267 (1992)

    MATH  MathSciNet  Google Scholar 

  12. A. Il’ichev, K. Kirchgässner, Universität Stutgart, Bericht 98/19 SFB 404 (1998)

  13. M. Coffey, Phys. Rev. B 54, 1279 (1996)

    ADS  Google Scholar 

  14. B. Tian, Y.T. Gao, Computers Math. Applic. 31, 115 (1996)

    MATH  Google Scholar 

  15. Y.T. Gao, B. Tian, Acta Mechanica 128, 137 (1998)

    MATH  MathSciNet  Google Scholar 

  16. W. Hong, Y. Jung, Phys. Lett. A 257, 149 (1999)

    MATH  MathSciNet  ADS  Google Scholar 

  17. B. Tian, Int. J. Mod. Phys. C 10, 1089 (1999)

    MATH  ADS  Google Scholar 

  18. G. Das, J. Sarma, Phys. Plasmas 6, 4394 (1999)

    MathSciNet  ADS  Google Scholar 

  19. W. Hong, Y. Jung, Z. Naturforsch. A 54, 272 (1999)

    Google Scholar 

  20. W. Hong, Y. Jung, Z. Naturforsch. A 54, 549 (1999)

    Google Scholar 

  21. B. Tian, Y.T. Gao, Int. J. Mod. Phys. C 15, 545 (2004)

    MATH  ADS  Google Scholar 

  22. M.P. Barnett, J.F. Capitani, J. Von Zur Gathen, J. Gerhard, Int. J. Quantum Chem. 100, 80 (2004); Sirendaoreji, J. Phys. A 32, 6897 (1999); W.P. Hong, S.H. Park, Int. J. Mod. Phys. C 15, 363 (2004); F.D. Xie, X.S. Gao, Comm. Theor. Phys. 41, 353 (2004); B. Li, Y. Chen, H.N. Xuan, H.Q. Zhang, Appl. Math. Comput. 152, 581 (2004); Y.T. Gao, B. Tian, Phys. Plasmas 10, 4306 (2003); B. Tian, Y.T. Gao, Nuov. Cim. B 118, 175 (2003); B. Tian, Y.T. Gao, Computers Math. Applic. 45, 731 (2003)

    Google Scholar 

  23. W. Hong, M. Yoon, Z. Naturforsch. A 56, 366 (2001); B. Tian, W. Li, Y.T. Gao, Acta Mechanica 160, 235 (2003); R. Ibrahim, Chaos, Solitons & Fractals 16, 675 (2003); R. Ibrahim, IMA J. Appl. Math. 68, 523 (2003)

    Google Scholar 

  24. W.T. Wu, J. Sys. Sci. Math. Sci. 4, 207 (1984); W.T. Wu, Kexue Tongbao 31, 1 (1986)

    Google Scholar 

  25. Z.Y. Yan, H.Q. Zhang, Phys. Lett. A 252, 291, 1999; J. Phys. A 34, 1785 (2001)

    ADS  Google Scholar 

  26. X.S. Gao, Adv. Math. 30(5), 385 (2001, in Chinese)

    Google Scholar 

  27. Handbook of Mathematics Working Group, Handbook of Mathematics, 4th edn. (China Higher Education Press, Beijing, 1990)

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Author information

Authors and Affiliations

  1. School of Science, Beijing University of Posts and Telecommunications, P.O. Box 122, 100876, Beijing, China

    Bo Tian

  2. State Key Laboratory of Software Development Environment, Beijing University of Aeronautics and Astronautics, 100083, Beijing, China

    Bo Tian & Yi-Tian Gao

  3. CCAST (World Lab.), P.O. Box 8730, 100080, Beijing, China

    Yi-Tian Gao

  4. Ministry of Education Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics, 100083, Beijing, China

    Yi-Tian Gao

Authors
  1. Bo Tian
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  2. Yi-Tian Gao
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Corresponding author

Correspondence to Yi-Tian Gao.

Additional information

Received: 21 July 2004, Published online: 23 December 2004

PACS:

47.11. + j Computational methods in fluid dynamics - 05.45.Yvi Solitons - 47.35. + i Hydrodynamic waves - 02.70.Wz Symbolic computation (computer algebra)

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Tian, B., Gao, YT. (2 + 1) dimensional Hărăgus-Courcelle-Il’ichev model for the liquid surface waves in the presence of sea ice or surface tension: Bäcklund transformation, exact solutions and possibly observable effects. Eur. Phys. J. B 42, 441–450 (2004). https://doi.org/10.1140/epjb/e2004-00402-8

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  • DOI: https://doi.org/10.1140/epjb/e2004-00402-8

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