Perturbation Analysis for Wave Equation of A Nonlinear Elastic Rod

LÜ Ke-pu; GUO Peng; ZHANG Lei; YI Jin-qiao; DUAN Wen-shan

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2006 > 27(9): 1079-1083

LÜ Ke-pu, GUO Peng, ZHANG Lei, YI Jin-qiao, DUAN Wen-shan. Perturbation Analysis for Wave Equation of A Nonlinear Elastic Rod[J]. Applied Mathematics and Mechanics, 2006, 27(9): 1079-1083.

Citation:

LÜ Ke-pu, GUO Peng, ZHANG Lei, YI Jin-qiao, DUAN Wen-shan. Perturbation Analysis for Wave Equation of A Nonlinear Elastic Rod[J]. Applied Mathematics and Mechanics, 2006, 27(9): 1079-1083.

Citation:

LÜ Ke-pu, GUO Peng, ZHANG Lei, YI Jin-qiao, DUAN Wen-shan. Perturbation Analysis for Wave Equation of A Nonlinear Elastic Rod[J]. Applied Mathematics and Mechanics, 2006, 27(9): 1079-1083.

PDF( 233 KB)

Perturbation Analysis for Wave Equation of A Nonlinear Elastic Rod

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

Received Date: 2005-12-19
Rev Recd Date: 2006-03-28
Publish Date: 2006-09-15

Abstract

Abstract

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

FullText(HTML)

References(7)

References

[1]	庄蔚,张善元.非线性弹性杆中的应变孤波[J].力学学报,1988,20(1):58—67.
[2]	庄蔚,杨桂通.孤波在非线性杆中的传播[J].应用数学和力学,1986,7(7):571—581.
[3]	DUAN Wen-shan,ZHAO Jing-bao.Solitary waves in a quadratic nonlinear elastic rod[J].Chaos,Solitons and Fractals,2000,11(8):1265—1267. doi: 10.1016/S0960-0779(99)00014-4
[4]	谷内俊弥,西原功修(日).非线性波动[M].徐福元,张家泰,丁启明译. 北京：原子能出版社,1981,99—119.
[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. doi: 10.1143/JPSJ.24.941
[6]	戴世强.约化摄动法和非线性波远场分析[J].力学进展,1982,12(1):2—23.[JP3]. 吕克璞,孙建安,段文山，等.超KdV方程的减缩摄动解法[J].应用数学和力学,2001,22(7):753—757.
[8]	倪皖荪，魏荣爵.水槽中的孤波[M].上海：上海科技教育出版社,1997,104—112.