Commun. Comput. Phys.,
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Volume 4.

Progress of Pattern Dynamics in Plasma Waves

B. Qiao 1, C. T. Zhou 2*, X. T. He 2, C. H. Lai 3

1 Center for Plasma Physics, Department of Physics and Astronomy, Queen's University Belfast, Belfast BT7 1NN, UK; Department of Physics, National University of Singapore, Singapore 117542; Institute of Applied Physics and Computational Mathematics, P. O. Box 8009, Beijing 100088, China.
2 Institute of Applied Physics and Computational Mathematics, P. O. Box 8009, Beijing 100088, China; Center for Applied Physics and Technology, Peking University, Beijing 100871, China; Institute for Fusion Theory and Simulation, Zhejiang University, Hangzhou 310027, China.
3 Department of Physics and Beijing-Hong Kong-Singapore Joint Centre for Nonlinear and Complex Systems (Singapore), National University of Singapore, Singapore 117542.

Received 29 February 2008; Accepted (in revised version) 8 July 2008
Available online 9 September 2008


This paper is concerned with the pattern dynamics of the generalized nonlinear Schrodinger equations (NSEs) related with various nonlinear physical problems in plasmas. Our theoretical and numerical results show that the higher-order nonlinear effects, acting as a Hamiltonian perturbation, break down the NSE integrability and lead to chaotic behaviors. Correspondingly, coherent structures are destroyed and replaced by complex patterns. Homoclinic orbit crossings in the phase space and stochastic partition of energy in Fourier modes show typical characteristics of the stochastic motion. Our investigations show that nonlinear phenomena, such as wave turbulence and laser filamentation, are associated with the homoclinic chaos. In particular, we found that the unstable manifolds $W^{(u)}$ possessing the hyperbolic fixed point correspond to an initial phase $\theta=45^\circ$ and $225^\circ$, and the stable manifolds $W^{(s)}$ correspond to $\theta =135^\circ$ and $315^\circ$.

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PACS: 47.54.-r, 05.45.Yv, 52.25.Gj, 52.35.Mw
Key words: Pattern dynamics, homoclinic chaos, nonlinear Schrodinger equations, plasma waves.

*Corresponding author.
Email: (B. Qiao), (C. T. Zhou), (X. T. He), (C. H. Lai)

The Global Science Journal