# Effect of the dynamical phases on the nonlinear amplitudes&#x27; evolution - Nonlinear Sciences > Exactly Solvable and Integrable Systems

Effect of the dynamical phases on the nonlinear amplitudes&#x27; evolution - Nonlinear Sciences > Exactly Solvable and Integrable Systems - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

Abstract: In this Letter we show how the nonlinear evolution of a resonant triaddepends on the special combination of the modes- phases chosen according to theresonance conditions. This phase combination is called dynamical phase. Itsevolution is studied for two integrable cases: a triad and a cluster formed bytwo connected triads, using a numerical method which is fully validated bymonitoring the conserved quantities known analytically. We show that dynamicalphases, usually regarded as equal to zero or constants, play a substantial rolein the dynamics of the clusters. Indeed, some effects are i to diminish theperiod of energy exchange $\tau$ within a cluster by 20$%$ and more; ii todiminish, at time scale $\tau$, the variability of wave energies by 25$%$ andmore; iii to generate a new time scale, $T >> \tau$, in which we observeconsiderable energy exchange within a cluster, as well as a periodic behaviourwith period $T$ in the variability of modes- energies. These findings can beapplied, for example, to the control of energy input, exchange and output inTokamaks; for explanation of some experimental results; to guide and improvethe performance of experiments; to interpret the results of numericalsimulations, etc.

Autor: Miguel D. Bustamante, Elena Kartashova

Fuente: https://arxiv.org/