Exploding dissipative solitons in reaction-diffusion systems

Descalzi, Orazio; Akhmediev, Nail; Brand, Helmut R.

doi:10.1103/physreve.88.042911

Cited by 17 publications

(3 citation statements)

References 56 publications

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“…Although originally discovered in models of Nonlinear Optics such as the nonlinear Schrödinger equation (NLS) with dissipation and quintic nonlinearities, they have been found as well in other models in wide regions of parameter space. They can also appear in reaction-diffusion systems of multiple species if strong cross-diffusion is present [7]. More interestingly, explosions of solitons have been observed in several experiments of propagation of strong light pulses: in Ti:sapphire mode-locked lasers [8] and in double-clad ytterbium-doped fibers [9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 96%

A new kind of chaotic diffusion: anti-persistent random walks of explosive dissipative solitons

2019

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The solitons that exist in nonlinear dissipative media have properties very different from the ones that exist in conservative media and are modeled by the nonlinear Schrödinger equation. One of the surprising behaviors of dissipative solitons is the occurrence of explosions: sudden transient enlargements of a soliton, which as a result induce spatial shifts. In this work using the complex Ginzburg-Landau equation in one dimension, we address the long-time statistics of these apparently random shifts. We show that the motion of a soliton can be described as an anti-persistent random walk with a corresponding oscillatory decay of the velocity correlation function. We derive two simple statistical models, one in discrete and one in continuous time, which explain the observed behavior. Our statistical analysis benchmarks a future microscopic theory of the origin of this new kind of chaotic diffusion.

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Section: Introductionmentioning

confidence: 96%

A new kind of chaotic diffusion: anti-persistent random walks of explosive dissipative solitons

2019

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“…By dissipative solitons, we mean solutions whose existence is based on the balance of nonlinearity, dispersion, gain and loss [6]. Dissipative solitons have been studied either experimentally, in systems such as binary fluid convection [7][8][9], surface reactions [3,10], granular matter [11,12], starch suspensions [13,14], nonlinear optics [15][16][17] and sheared electroconvection in liquid crystals [18], or theoretically by means of prototype equations, such as envelope equations of the Ginzburg-Landau-type , order parameter equations [41][42][43] or reaction-diffusion equations [44][45][46][47][48][49]. The studies on localized solutions in Ginzburg-Landautype equations include studies in one [19][20][21]23,24,[26][27][28][29]33,34,[36][37][38][39] as well as in two [19,22,23,25,26,30,31,…”

Section: Introductionmentioning

confidence: 99%

Non-unique results of collisions of quasi-one-dimensional dissipative solitons

Descalzi

Brand

2015

Phil. Trans. R. Soc. A.

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We investigate collisions of quasi-one-dimensional dissipative solitons (DSs) for a large class of initial conditions, which are not temporally asymptotic quasi-one-dimensional DSs. For the case of sufficiently small approach velocity and sufficiently large values of the dissipative cross-coupling between the counter-propagating DSs, we find non-unique results for the outcome of collisions. We demonstrate that these non-unique results are intrinsically related to a modulation instability along the crest of the quasi-one-dimensional objects. As a model, we use coupled cubic-quintic complex Ginzburg-Landau equations. Among the final results found are stationary and oscillatory compound states as well as more complex assemblies consisting of quasi-one-dimensional and localized states. We analyse to what extent the final results can be described by the solutions of one cubic-quintic complex Ginzburg-Landau equation with effective parameters.

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“…Another important feature is that their amplitude do not exceed a certain limit. Exploding solitons also exist in other systems, such as in reaction-diffusion systems [4,5]. It is presently an emerging field of study in physics [6][7][8].…”

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confidence: 99%