Moving discrete breathers?

Flach, Sergej; Kladko, K.

doi:10.1016/s0167-2789(98)00274-7

Cited by 83 publications

(53 citation statements)

References 22 publications

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“…The numerical solution of the coupled DNLSEs (18)- (19), with the initial condition ψ (1)j (t = 0) = Ψ V j (t = 0) given by (20) and Λ = Λ sol , turns out to be in excellent agreement with (22) for different values of p, as shown in Fig. 2 for ω constant.…”

Section: B 1d Chainmentioning

confidence: 72%

“…In 1D, the DNLSE is not integrable [17]; however, and as concerns the homogeneous case (V j = 0), solitonlike wavepackets exist and can propagate for a long time as stable objects, as it can be shown, e.g., by variational approaches [19,20]. Furthermore, the dynamics of such traveling pulses has been investigated in detail in the literature [21,22,23,24,25]. Based on the above discussion, here we consider the dynamics of a multicomponent BEC in an optical lattice described by a system of coupled DNLSEs, the different BEC components being different hyperfine levels [26].…”

Section: Introductionmentioning

confidence: 99%

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Soliton dynamics in linearly coupled discrete nonlinear Schrödinger equations

Trombettoni

Nistazakis

Rapti

et al. 2009

Mathematics and Computers in Simulation

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We study soliton dynamics in a system of two linearly coupled discrete nonlinear Schrödinger equations, which describe the dynamics of a two-component Bose gas, coupled by an electromagnetic field, and confined in a strong optical lattice. When the nonlinear coupling strengths are equal, we use a unitary transformation to remove the linear coupling terms, and show that the existing soliton solutions oscillate from one species to the other. When the nonlinear coupling strengths are different, the soliton dynamics is numerically investigated and the findings are compared to the results of an effective two-mode model. The case of two linearly coupled Ablowitz-Ladik equations is also investigated.

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Section: B 1d Chainmentioning

confidence: 72%

Section: Introductionmentioning

confidence: 99%

Soliton dynamics in linearly coupled discrete nonlinear Schrödinger equations

Trombettoni

Nistazakis

Rapti

et al. 2009

Mathematics and Computers in Simulation

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show abstract

“…A detailed analysis of possible resonances has been carried out in [8,9]. It follows that one has to avoid resonances of the velocity V with phase velocities v ph of small amplitude plane waves (where the linear spectra which have been modified, as compared with the original underlying one).…”

Section: Why Only Time-periodic Orbits?mentioning

confidence: 99%

Discrete Breathers with Dissipation

Flach

Gorbach

2008

Lecture Notes in Physics

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The interplay between discreteness and nonlinearity leads to the emergence of a new class of nonlinear excitations, viz. discrete breathers. These time-periodic and spatially localized excitations correspond to generic exact solutions of the underlying nonlinear lattice models. Discrete breathers are not confined to certain lattice dimensions, nor are they sensitive to the particular type of nonlinearity in the system. They are usually dynamically and structurally stable and emerge in a variety of physical systems, ranging from lattice vibrations and magnetic excitations in crystals to light propagation in photonic structures and cold atom dynamics in periodic optical traps. Basic properties of discrete breathers, including spatial localization and stability, are briefly discussed in this chapter. Special focus is placed on a subclass of dissipative discrete breathers. Dissipation eliminates extended waves and allows for various resonances of discrete breathers with damped cavity modes. We discuss applications of the discrete breather concept in systems where dissipation is not only unavoidable but essential in order to observe and manipulate discrete breathers, and in order to use them for spectroscopic tools, amongst others.

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“…The question of the existence of moving solitons in the DNLS equation has been the subject of debate for some time [7,8,9,10,11,12,13,14,15,16,17,18,19]. Recently, Gómez-Gardeñes, Floría, Falo, Peyrard and Bishop [20,21] have demonstrated that the stationary motion of pulses in the cubic one-site DNLS (the 'standard' DNLS) is only possible over an oscillatory background consisting of a superposition of plane waves.…”

Section: Introductionmentioning

confidence: 99%

Moving solitons in the discrete nonlinear Schrödinger equation

Oxtoby

Barashenkov

2007

Phys. Rev. E

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Using the method of asymptotics beyond all orders, we evaluate the amplitude of radiation from a moving small-amplitude soliton in the discrete nonlinear Schrödinger equation. When the nonlinearity is of the cubic type, this amplitude is shown to be nonzero for all velocities and therefore small-amplitude solitons moving without emitting radiation do not exist. In the case of a saturable nonlinearity, on the other hand, the radiation is found to be completely suppressed when the soliton moves at one of certain isolated 'sliding velocities'. We show that a discrete soliton moving at a general speed will experience radiative deceleration until it either stops and remains pinned to the lattice, or-in the saturable case-locks, metastably, onto one of the sliding velocities. When the soliton's amplitude is small, however, this deceleration is extremely slow; hence, despite losing energy to radiation, the discrete soliton may spend an exponentially long time travelling with virtually unchanged amplitude and speed.

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Moving discrete breathers?

Cited by 83 publications

References 22 publications

Soliton dynamics in linearly coupled discrete nonlinear Schrödinger equations

Soliton dynamics in linearly coupled discrete nonlinear Schrödinger equations

Discrete Breathers with Dissipation

Moving solitons in the discrete nonlinear Schrödinger equation

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