Skip to main content
SpringerLink
Log in

Perturbation analysis for wave equation of nonlinear elastic rod

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

The longitudinal oscillation of a nonlinear elastic rod with lateral inertia was studied. Based on the far field and simple wave theory, a nonlinear Schrödinger (NLS) equation was established under the assumption of small amplitude and long wavelength. It is found that there are NLS envelop solitons in this system. Finally the soliton solution of the NLS equation was presented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Zhuang wei, Zhang Shanyuan. The strain solitary waves in a nonlinear elastic rod[J]. Acta Mechanica Sinica, 1988, 20(1):58–67 (in Chinese).

    Google Scholar 

  2. Zhuang Wei, Zhang Guitong. The propagation of solitary waves in a nonlinear elastic rod[J]. Applied Mathematics and Mechanics (English Edition), 1986, 7(7):615–626 (in Chinese).

    Article  MATH  Google Scholar 

  3. Duan Wenshan, Zhao Jingbao. Solitary waves in a quadratic nonlinear elastic rod[J]. Chaos, Solitons and Fractals, 2000, 11(8):1265–1267.

    Article  MATH  Google Scholar 

  4. TaniutiT, Nisihara. Nonlinear Wave Propagation[M]. Xu Fuyuan, Zhang Jiatai, Ding Qiming (transls). Atomic Energy Press, Beijing, 1981, 99–119 (in Chinese).

    Google Scholar 

  5. Taniuti T, Wei C C. Reductive perturbation method in nonlinear wave propagation[J]. Journal of the Physical Society of Japan, 1968, 24(4):941–946.

    Google Scholar 

  6. Dai Shiqiang. Reductive perturbation method and far-field analysis of nonlinear wave[J]. Advances in Mechanics, 1982, 12(1):2–23 (in Chinese).

    Google Scholar 

  7. Lü Kepu, Sun Jian’an, Duan Wenshan, Zhao Jinbao. Reductive perturbation method of super KdV equations[J]. Applied Mathematics and Mechanics (English Edition), 2001, 22(7):846–850.

    Article  MATH  MathSciNet  Google Scholar 

  8. Ni Wansun, Wei Rongjue. Solitary Wave in Water Trough[M]. Shanghai Scientific and Technological Education Publishing House, Shanghai, 1997, 104–112 (in Chinese).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou, 730070, P. R. China

    Lü Ke-pu  (吕克璞) (Professor), Guo Peng  (郭鹏), Zhang Lei  (张磊), Yi Jin-qiao  (易金桥) & Duan Wen-shan  (段文山)

Authors
  1. Lü Ke-pu  (吕克璞)
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Guo Peng  (郭鹏)
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhang Lei  (张磊)
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yi Jin-qiao  (易金桥)
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Duan Wen-shan  (段文山)
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lü Ke-pu  (吕克璞).

Additional information

Communicated by DAI Shi-qiang

Project supported by the National Natural Science Foundation of China (No.10247008) and the Natural Science Foundation of Northwest Normal University (No.NWNU-KJCXGC-215)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lü, Kp., Guo, P., Zhang, L. et al. Perturbation analysis for wave equation of nonlinear elastic rod. Appl Math Mech 27, 1233–1238 (2006). https://doi.org/10.1007/s10483-006-0910-z

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-006-0910-z

Key words

Chinese Library Classification

2000 Mathematics Subject Classification

Search

Navigation