1973
DOI: 10.1088/0032-1028/15/2/005
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Dynamics of the non-linear interaction of magnetohydrodynamic waves

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Cited by 26 publications
(13 citation statements)
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“…The case of dissipative three-wave coupling was shown to present transition to chaotic behavior through well-known routes, as a cascade of period-doubling bifurcations of cycles [17], and intermittency, where stable periodic orbits abruptly take over chaotic attractors [18]. These analyses can be further extended for certain classes of four-wave parametric interactions, in which two waves participate simultaneously in two resonant triplets [19,20]. The conservative case of this problem was found to be exactly integrable, since it presents the same number of integrals of motion as the degrees of freedom, when the wave frequencies match exactly [21].…”
Section: Introductionmentioning
confidence: 98%
“…The case of dissipative three-wave coupling was shown to present transition to chaotic behavior through well-known routes, as a cascade of period-doubling bifurcations of cycles [17], and intermittency, where stable periodic orbits abruptly take over chaotic attractors [18]. These analyses can be further extended for certain classes of four-wave parametric interactions, in which two waves participate simultaneously in two resonant triplets [19,20]. The conservative case of this problem was found to be exactly integrable, since it presents the same number of integrals of motion as the degrees of freedom, when the wave frequencies match exactly [21].…”
Section: Introductionmentioning
confidence: 98%
“…Because C (1) is trivial, we begin with C (2) , equation (11) for n = 2. Inserting the transformations (12) and (42) into C (2) gives…”
Section: Beatified Constants Of Motionmentioning
confidence: 99%
“…Resonant four-wave coupling involves the interaction of two wave triplets. The presence of the second triplet having two waves in common with the first can either increase or stabilize the instability of the first triplet (Karplyuk et al 1973;Walters & Lewak 1977). Accordingly, we introduced a new resonance into the system by including a fourth wave f 4 , obeying the additional resonant conditions,…”
Section: Control Of Chaosmentioning
confidence: 99%