題 目： Influence of noise on dissipative solitons and their interaction
We give an overview of the influence of noise on spatially localized patterns and their interaction. Localized patterns include stationary dissipative solitons, oscillatory dissipative solitons with one and two frequencies as well as exploding dissipative solitons. The influence of noise on spatially localized structures of arbitrary length, which are localized due to the trapping mechanism, has been investigated in  and it was shown that the logarithm of the lifetime scales inversely with the noise intensity. Thus the picture of a noise-activated barrier crossing has been demonstrated. A long standing puzzle in the field of pattern formation has been the experimental observation of the partial annihilation of pulses in binary fluid convection  and during CO oxidation in surface reactions [3,4] it has been shown that already a small amount of additive noise can account for the experimental observation. The mechanism will be elucidated in the presentation. Recently it has been shown that a small amount of noise can induce explosions for dissipative solitons in the vicinity of the transition sequence from stationary dissipative solitons to exploding dissipative solitons via three different routes [6,7]. We also investigate the influence of large noise on the formation of localized patterns in the framework of the cubic-quintic complex Ginzburg-Landau equation. The interaction of localization and noise can lead to filling-in or noisy localized structures for fixed noise strength. To focus on the interaction between noise and localization we cover a region in parameter space, in particular subcriticality, for which stationary stable deterministic pulses do not exist . Possible experimental tests of the work presented for autocatalytic chemical reactions and bio-inspired systems are outlined. Finally we present some of our recent results on the influence of spatially homogeneous multiplicative noise on spatially localized solutions in nonequilibrium systems.
 H. Sakaguchi, H. R. Brand : Physica D - Nonlinear Phenomena 97, 274 (1996).
 P. Kolodner : Phys. Rev. A 44, 6466 (1991).
 H. H. Rotermund, S. Jakubith, A. von Oertzen, G. Ertl : Phys. Rev. Lett. 66, 3083 (1991).
 A. von Oertzen, A. S. Mikhailov, H. H. Rotermund, G. Ertl : J. Chem. Phys. B 102, 4966 (1998).
 O. Descalzi, J. Cisternas, D. Escaff, H. R. Brand : Phys. Rev. Lett. 102, 188302 (2009).
 C. Cartes, O. Descalzi, H. R. Brand : Phys. Rev. E 85, 015205 (2012).
 C. Cartes, O. Descalzi, H. R. Brand : Eur. Phys. J. Special Topics 223, 2145 (2014).
 O. Descalzi, C. Cartes, H. R. Brand : Phys. Rev. E 91, 020901 (2015).
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