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Periods of periodic travelling wave solutions for an elastic beam equation

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Abstract

The periods of the periodic travelling wave solutions for an elastic beam equation were studied. By the transformation of variables, the elastic beam equation was reduced to a planar differential system. The period function of the planar differential system is examined. It was proved that the period function is a monotonic function. Moreover, the asymptotic behaviour of the period function was also given.

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References

  1. K Konno, Y Ichikawa and W Wadati,  J. Phys. Soc. Jpn 50, 1025 (1981)

    Article  ADS  Google Scholar 

  2. R Gorder,  Prog. Theor. Phys. 128, 993 (2012)

    Article  ADS  Google Scholar 

  3. R Gorder,  J. Phys. Soc. Jpn 82, 064005 (2013)

    Article  ADS  Google Scholar 

  4. J Li, Y Zhang and G Chen,  Int. J. Bifurc. Chaos 19, 2249 (2009)

    Article  Google Scholar 

  5. M Wadati, K Konno and Y Ichikawa,  J. Phys. Soc. Jpn 47, 1698 (1979)

    Article  ADS  Google Scholar 

  6. M Lakshmaanan and S Ganesan,  Physica A 132, 117 (1985)

    Article  ADS  MathSciNet  Google Scholar 

  7. Z Li, X Geng and L Guan,  Math. Meth. Appl. Sci. 39, 734 (2016)

    Article  Google Scholar 

  8. Y Zhang, J Rao, Y Cheng and J He,  Physica D 399, 173 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  9. A Chen, C Tian and W Huang,  Appl. Math. Lett. 77, 101 (2018)

    Article  MathSciNet  Google Scholar 

  10. A Chen, C Zhang and W Huang,  Appl. Math. Lett. 121, 107381 (2021)

    Article  Google Scholar 

  11. A Chen, J Li and W Huang,  Nonliner Dyn. 63, 205 (2010)

    Article  Google Scholar 

  12. A Chen, L Guo and X Deng,  J. Differ. Equ. 261, 5324 (2016)

    Article  Google Scholar 

  13. L Guo and Y Zhao,  Disc. Contin. Dyn. Syst. 40, 4689 (2020)

    Article  Google Scholar 

  14. A Geyer and J Villadelprat,  J. Differ. Equ. 256, 2317 (2015)

    Article  ADS  Google Scholar 

  15. C Chicone,  J. Differ. Equ. 69, 310 (1987)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

The authors would like to thank the referee for very useful comments and suggestions. A Chen is supported by the Natural Science Foundation of Hunan Province (No. 2021JJ30166) and the National Natural Science Foundation of China (No. 11971163). X He is supported by the Key Project of Education Department of Hunan Province (21A0576).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Hunan First Normal University, Changsha,  410205, People’s Republic of China

    Aiyong Chen & Xiaokai He

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  1. Aiyong Chen
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  2. Xiaokai He
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Correspondence to Xiaokai He.

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Chen, A., He, X. Periods of periodic travelling wave solutions for an elastic beam equation. Pramana - J Phys 96, 203 (2022). https://doi.org/10.1007/s12043-022-02451-7

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  • DOI: https://doi.org/10.1007/s12043-022-02451-7

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