Thermalization of the dispersive three-wave interaction

• Published in: Europhysics letters Vol. 79; no. 6; pp. 64001 - 64001p6
• Main Authors: Lagrange, S, Jauslin, H. R, Picozzi, A
• Format: Journal Article
• Language: English
• Published: IOP Publishing 01.09.2007; EDP Sciences; European Physical Society / EDP Sciences / Società Italiana di Fisica / IOP Publishing
• Subjects: 05.45.-a; 42.25.Kb; 42.65.Sf
• ISSN: 0295-5075; 1286-4854
• DOI: 10.1209/0295-5075/79/64001

We investigate the role of dispersion effects on the long-term evolution of the nonlinear three-wave interaction. We show that the three waves exhibit, as a general rule, an irreversible evolution towards a thermodynamic equilibrium state in which they propagate with identical velocities. As a result of this thermalization process, the three-wave system is driven away from spatio-temporal resonance, so that the equilibrium state does not satisfy the (phase-matching) resonant conditions of energy and momentum conservation for the averaged frequencies. Moreover, we show that the interplay between temporal dispersion and spatial diffraction leads to the emergence of a peculiar equilibrium state characterized by an X-shaped spatio-temporal spectrum.