The coherence of waves in periodic systems (lattices) is crucial to their dynamics, as interference effects, such as Bragg reflections, largely determine their propagation. Whereas linear systems allow superposition, nonlinearity introduces a non-trivial interplay between localization effects, coupling between lattice sites, and incoherence. Until recently, all research on solitary waves (solitons) in nonlinear lattices has involved only coherent waves. In such cases, linear dispersion or diffraction of wave packets can be balanced by nonlinear effects, resulting in coherent lattice (or ‘discrete’) solitons1,2; these have been studied in many branches of science3,4,5,6,7,8,9,10,11. However, in most natural systems, waves with only partial coherence are more common, because fluctuations (thermal, quantum or some other) can reduce the correlation length to a distance comparable to the lattice spacing. Such systems should support random-phase lattice solitons displaying distinct features12. Here we report the experimental observation of random-phase lattice solitons, demonstrating their self-trapping and local periodicity in real space, in addition to their multi-peaked power spectrum in momentum space. We discuss the relevance of such solitons to other nonlinear periodic systems in which fluctuating waves propagate, such as atomic systems, plasmas and molecular chains.
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This work was supported by the Israeli Science Foundation, the Israel–USA Binational Science Foundation, and by the German-Israeli DIP Project. O.C. acknowledges the generous support of the Israeli Ministry of Science through the Eshkol Fellowship.
The authors declare that they have no competing financial interests.
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Cohen, O., Bartal, G., Buljan, H. et al. Observation of random-phase lattice solitons. Nature 433, 500–503 (2005). https://doi.org/10.1038/nature03267
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