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Numerical simulation of standing solitons and their interaction

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Abstract

Standing soliton was studied by numerical simulation of its governing equation, a cubic Schrödiger equation with a complex conjugate term, which was derived by Miles and was accepted. The value of linear damping in Miles equation was studied. Calculations showed that linear damping effects strongly on the formation of a standing soliton and Laedke and Spatschek stable condition is only a necessary condition, but not a sufficient one. The interaction of two standing solitons was simulated. Simulations showed that the interaction pattern depends on system parameters. Calculations for the different initial condition and its development indicated that a stable standing soliton can be formed only for proper initial disturbance, otherwise the disturbance will disappear or develop into several solitons.

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References

  1. WU Jun-ru, Keolian R, Rudnick I. Observation of a non-propagating hydrodynamic soliton [J].Phys Rev Lett, 1984,52: 1421–1424.

    Article  Google Scholar 

  2. Larraza A, Putterman S. Theory of non-propagating surface-wave solitons [J].J Fluid Mech, 1984,148: 443–449.

    Article  MATH  Google Scholar 

  3. Miles J W. Parametrically excited solitary waves [J].J Fluid Mech, 1984,148: 451–460.

    Article  MATH  MathSciNet  Google Scholar 

  4. Laedke E W, Spatschek K H. On localized solution in nonlinear Faraday resonance [J].J Fluid Mech, 1991,223: 589–601.

    Article  MATH  MathSciNet  Google Scholar 

  5. Chen X, Wei R J, Wang B R. Chaos in non-propagating hydrodynamics solitons [J].Phys Rev, 1996,53: 6016–6020.

    Article  Google Scholar 

  6. Chen W Z, Wei R J, Wang B R. Non-propagating interface solitary wave in fluid [J].Phys Lett A, 1995,208: 197–200.

    Article  MATH  MathSciNet  Google Scholar 

  7. Chen W Z. Experimental observation of self-localized structure in granular material [J].Phys Lett A, 1995,196: 321–325.

    Article  Google Scholar 

  8. CUI Hong-nong, et al. Observation and experiment of non-propagating solitary wave [J].Acta of Xiangtan University in Nature Science, 1986,4: 27–34. (in Chinese)

    Google Scholar 

  9. CUI Hong-nong, et al. Study on the characteristic of non-propagating solitary wave [J].J Hydrodynamics, 1991,6(1): 18–25. (in Chinese)

    Google Scholar 

  10. ZHOU Xian-chu, CUI Hong-nong. The effect of surface tension no non-propagating solitary waves [J].Science in China A, 1992,12: 1269–1276.

    Google Scholar 

  11. ZHOU Xian-chu. Non-propagating soliton and surface tension [J].Acta Mech Sinica, 1998,30 (6): 672–675. (in Chinese)

    Google Scholar 

  12. YAN Jia-ren, HUANG Guo-xiang. Non-propagating solitary wave on interface of two layer fluid in rectangular wave guide [J].Acta Phys, 1988,37: 874–880. (in Chinese)

    Google Scholar 

  13. Yan J R, Mei Y P. Interaction between two Wu's solitons [J].Europhys Lett, 1993,23: 335–340.

    Google Scholar 

  14. ZHOU Xian-chu, TANG Shi-min, QIN Su-di. The stability of a standing soliton [A]. In: CHIEN Wei-zang, GUO Zhong-heng, GUO You-zhong Eds.Proc 2 nd Int Conf of Nonlinear Mech[C]. Beijing: Peking University Press, 1993, 455–458.

    Google Scholar 

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Authors and Affiliations

  1. Institute of Mechanics, Chinese Academy of Sciences, 100080, Beijing, P R China

    Zhou Xian-chu Professor & Rui Yi

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  1. Zhou Xian-chu Professor
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  2. Rui Yi
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Additional information

Paper from ZHOU Xian-chu, Member of Editorial Committee, AMM

Foundation item: the National Natural Science Foundation of China (19572071); the National Basic Research Project “Nonlinear Science”

Biography: ZHOU Xian-chu (1939-)

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Xian-chu, Z., Yi, R. Numerical simulation of standing solitons and their interaction. Appl Math Mech 21, 1371–1380 (2000). https://doi.org/10.1007/BF02459215

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  • DOI: https://doi.org/10.1007/BF02459215

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