The truncation model of the derivative nonlinear Schroedinger equation

Journal Article · Wed Apr 15 04:00:00 EDT 2009 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.3093383· OSTI ID:21276981

Sanchez-Arriaga, G ^[1]; Hada, T ^[2]; Nariyuki, Y ^[3]

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1. Escuela Tecnica Superior de Ingenieros Aeronauticos, Universidad Politecnica de Madrid, Plaza Cardenal Cisneros, 28040 Madrid (Spain)
2. Department of Earth System Science and Technology, Kyushu University, Fukuoka 816-8580 (Japan)
3. Department of Electrical Engineering, Kochi National College of Technology, Kochi 783-8508 (Japan)

The derivative nonlinear Schroedinger (DNLS) equation is explored using a truncation model with three resonant traveling waves. In the conservative case, the system derives from a time-independent Hamiltonian function with only one degree of freedom and the solutions can be written using elliptic functions. In spite of its low dimensional order, the truncation model preserves some features from the DNLS equation. In particular, the modulational instability criterion fits with the existence of two hyperbolic fixed points joined by a heteroclinic orbit that forces the exchange of energy between the three waves. On the other hand, numerical integrations of the DNLS equation show that the truncation model fails when wave energy is increased or left-hand polarized modulational unstable modes are present. When dissipative and growth terms are added the system exhibits a very complex dynamics including appearance of several attractors, period doubling bifurcations leading to chaos as well as other nonlinear phenomenon. In this case, the validity of the truncation model depends on the strength of the dissipation and the kind of attractor investigated.

• OSTI ID: 21276981
• Journal Information: Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 4 Vol. 16; ISSN PHPAEN; ISSN 1070-664X
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
HAMILTONIAN FUNCTION
NONLINEAR PROBLEMS
PLASMA INSTABILITY
PLASMA WAVES
SCHROEDINGER EQUATION
TRAVELLING WAVES