The triple-degenerate derivative nonlinear Schrödinger (TDNLS) system modified with resistive wave damping and growth is truncated to study the coherent coupling of four waves, three Alfven and one acoustic, near resonance. In the conservative case, the truncation equations derive from a time independent Hamiltonian function with two degrees of freedom. Using a Poincare map analysis, two parameters regimes are explored. In the first regime we check how the modulational instability of the TDNLS system affects to the dynamics of the truncation model, while in the second one the exact triple degenerated case is discussed. In the dissipative case, the truncation model gives rise to a six dimensional flow with five free parameters. Computing some bifurcation diagrams the dependence with the sound to Alfven velocity ratio as well as the Alfven modes involved in the truncation is analyzed. The system exhibits a wealth of dynamics including chaotic attractor, several kinds of bifurcations, and crises. The truncation model was compared to numerical integrations of the TDNLS system.
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April 2009
Research Article|
April 03 2009
Truncation model in the triple-degenerate derivative nonlinear Schrödinger equation
G. Sánchez-Arriaga;
G. Sánchez-Arriaga
1Escuela Técnica Superior de Ingenieros Aeronáuticos,
Universidad Politécnica de Madrid
, Plaza Cardenal Cisneros, 28040 Madrid, Spain
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T. Hada;
T. Hada
2Department of Earth System Science and Technology,
Kyushu University
, Fukuoka 816-8580, Japan
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Y. Nariyuki
Y. Nariyuki
3Department of Electrical Engineering,
Kochi National College of Technology
, Kochi 783-8508, Japan
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Phys. Plasmas 16, 042303 (2009)
Article history
Received:
November 14 2008
Accepted:
February 11 2009
Connected Content
A companion article has been published:
The truncation model of the derivative nonlinear Schrödinger equation
Citation
G. Sánchez-Arriaga, T. Hada, Y. Nariyuki; Truncation model in the triple-degenerate derivative nonlinear Schrödinger equation. Phys. Plasmas 1 April 2009; 16 (4): 042303. https://doi.org/10.1063/1.3093394
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