Transition to chaos in the conservative four-wave parametric interactions

Physica D: Nonlinear Phenomena

Volumn 110, Issue 3-4, 1997, Pages 277-288

  Pakter, R ^a,b   Lopes, S R ^c   Viana, R L ^c  

^a UNIVERSITY OF SÃO PAULO   (Brazil)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^c FEDERAL UNIVERSITY OF PARANÁ   (Brazil)

Author keywords

Hamiltonian chaos; Mode coupling; Nonlinear optics; Plasma

Indexed keywords

EID: 22244434522     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(97)00130-9     Document Type: Article

References (15)

1. W.L. Kruer, The Physics of Laser Plasma Interactions (Addison-Wesley, Redwood City, 1988).
2. A.C.-L. Chian and F.B. Rizzato, Coupling of electromagnetic filamentation instability and electrostatic Langmuir parametric instabilities in laser-plasma interactions, J. Plasma Phys. 51 (1994) 61-73.
3. A.C.-L. Chian, S.R. Lopes and M.V. Alves, Generation of auroral whistler-mode radiation via nonlinear coupling of Langmuir waves and Alfvén waves, Astron. Astrophys. 290 (1994) L13-L16.
4. Y.R. Shen, The Principle of Nonlinear Optics (Wiley, New York, 1984).
5. A. Yariv, Quantum Electronics (Wiley, New York, 1989).
6. R. Sugihara, Interaction between an electromagnetic wave, plasma waves, and an ion acoustic wave, Phys. Fluids 11 (1968) 178-184.
7. K.S. Karplyuk, V.N. Oraevskii and V.P. Pavlenko, Dynamics of the nonlinear interaction of magnetohydrodynamic waves, J. Plasma Phys. 15 (1973) 113-124.
8. D. Walters and G.J. Lewak, Dynamics of four coupled plasma waves to second order, J. Plasma Phys. 18 (1977) 525-536.
9. F.J. Romeiras, Integrability of double three-wave interaction, Phys. Lett. A 93 (1983) 227-229.
10. S.R. Lopes and A.C.-L. Chian, Controlling chaos in nonlinear three-wave coupling, Phys. Rev. E 54 (1996) 170.
11. J.M. Wersinger, J.M. Finn and E. Ott, Bifurcations and strange behavior in instability saturation by nonlinear mode coupling, Phys. Rev. Lett. 44 (1980) 453-456.
12. A.C.-L. Chian, S.R. Lopes and J.R. Abalde, Hamiltonian chaos in two coupled three-wave parametric interactions with quadratic nonlinearity, Physica D 99 (1996) 269-275.
13. A.J. Lichtenberg and M.A. Lieberman, Regular and Stochastic Motion (Springer, New York, 1983).
14. J. Hietarinta, Direct methods for the search of the second invariant, Phys. Rep. 147 (1987) 87.
15. R. Pakter, I.L. Caldas, F. Couto, T. Caetano and F.B. Rizzato, Chaotic dynamics induced by space-charge waves in cyclotron resonance accelerators, Phys. Rev. E 54 (1996) 4202.