Chaos in the perturbed Korteweg-de Vries equation with nonlinear terms of higher order

doi:10.1088/1674-1056/19/3/030203

中国物理B ›› 2010, Vol. 19 ›› Issue (3): 30203-030203.doi: 10.1088/1674-1056/19/3/030203

Chaos in the perturbed Korteweg-de Vries equation with nonlinear terms of higher order

潘伟珍, 宋向炯, 俞军

Department of Physics, Shaoxing University, Shaoxing 312000, China

收稿日期:2008-12-17 修回日期:2009-08-02 出版日期:2010-03-15 发布日期:2010-03-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No.~10875078) and the Natural Science Foundation of Zhejiang Province, China (Grant No.~Y7080455).

Chaos in the perturbed Korteweg-de Vries equation with nonlinear terms of higher order

Pan Wei-Zhen(潘伟珍), Song Xiang-Jiong(宋向炯), and Yu Jun(俞军)^†ger

Department of Physics, Shaoxing University, Shaoxing 312000, China

Received:2008-12-17 Revised:2009-08-02 Online:2010-03-15 Published:2010-03-15
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No.~10875078) and the Natural Science Foundation of Zhejiang Province, China (Grant No.~Y7080455).

摘要/Abstract

摘要： The dynamical behaviour of the generalized Korteweg-de Vries (KdV) equation under a periodic perturbation is investigated numerically. The bifurcation and chaos in the system are observed by applying bifurcation diagrams, phase portraits and Poincaré maps. To characterise the chaotic behaviour of this system, the spectra of the Lyapunov exponent and Lyapunov dimension of the attractor are also employed.

Abstract: The dynamical behaviour of the generalized Korteweg-de Vries (KdV) equation under a periodic perturbation is investigated numerically. The bifurcation and chaos in the system are observed by applying bifurcation diagrams, phase portraits and Poincaré maps. To characterise the chaotic behaviour of this system, the spectra of the Lyapunov exponent and Lyapunov dimension of the attractor are also employed.

Key words: generalized KdV equation, bifurcation, chaos

中图分类号: (Solitons)

05.45.Yv

05.45.Pq (Numerical simulations of chaotic systems) 05.45.Gg (Control of chaos, applications of chaos) 02.30.Oz (Bifurcation theory) 02.30.Uu (Integral transforms)

潘伟珍, 宋向炯, 俞军. Chaos in the perturbed Korteweg-de Vries equation with nonlinear terms of higher order[J]. 中国物理B, 2010, 19(3): 30203-030203.

Pan Wei-Zhen(潘伟珍), Song Xiang-Jiong(宋向炯), and Yu Jun(俞军). Chaos in the perturbed Korteweg-de Vries equation with nonlinear terms of higher order[J]. Chin. Phys. B, 2010, 19(3): 30203-030203.

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Chaos in the perturbed Korteweg-de Vries equation with nonlinear terms of higher order

Chaos in the perturbed Korteweg-de Vries equation with nonlinear terms of higher order

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