Nonlinear lattice waves in heterogeneous media

Laptyeva, T. V.; Ivanchenko, Mikhail; Flach, Sergej

doi:10.1088/1751-8113/47/49/493001

Cited by 64 publications

(69 citation statements)

References 123 publications

(476 reference statements)

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“…Experimental evidences of such subdiffusive spreadings in Bose-Einstein condensates were provided in [55]. Subdiffusive spreading was also numerically observed for two-dimensional disordered lattices [14,33,44].…”

Section: Introductionmentioning

confidence: 95%

Characteristics of chaos evolution in one-dimensional disordered nonlinear lattices

2018

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We numerically investigate the characteristics of chaos evolution during wave packet spreading in two typical one-dimensional nonlinear disordered lattices: the Klein-Gordon system and the discrete nonlinear Schrödinger equation model. Completing previous investigations [38] we verify that chaotic dynamics is slowing down both for the so-called 'weak' and 'strong chaos' dynamical regimes encountered in these systems, without showing any signs of a crossover to regular dynamics. The value of the finite-time maximum Lyapunov exponent Λ decays in time t as Λ ∝ t α Λ , with αΛ being different from the αΛ = −1 value observed in cases of regular motion. In particular, αΛ ≈ −0.25 (weak chaos) and αΛ ≈ −0.3 (strong chaos) for both models, indicating the dynamical differences of the two regimes and the generality of the underlying chaotic mechanisms. The spatiotemporal evolution of the deviation vector associated with Λ reveals the meandering of chaotic seeds inside the wave packet, which is needed for obtaining the chaotization of the lattice's excited part.

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Section: Introductionmentioning

confidence: 95%

Characteristics of chaos evolution in one-dimensional disordered nonlinear lattices

2018

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“…The appearance and/or the destruction of Anderson localization in linear and nonlinear disordered systems, as well as the properties of energy propagation in such models, have attracted extensive attention in theory, numerical simulations and experiments, especially in recent years . a e-mail: snybob001@myuct.ac.za b e-mail: haris.skokos@uct.ac.za Studies of disordered versions of two basic, nonlinear Hamiltonian lattice models, namely the Klein-Gordon (KG) oscillator lattice and the discrete nonlinear Schrödinger equation (DNLS), revealed the existence of various dynamical behaviors, the so-called 'weak' and 'strong chaos' spreading regimes, as well as the 'selftrapping' regime and determined the statistical characteristics of energy propagation and chaos in these systems [12,13,15,33,[17][18][19]23,24,26,30,32]. One basic outcome of these studies is that energy propagation in disordered lattices is a chaotic process which, in general, results in the destruction of Anderson localization.…”

Section: Introductionmentioning

confidence: 99%

Computational efficiency of symplectic integration schemes: application to multidimensional disordered Klein–Gordon lattices

Senyange

Skokos

2018

Eur. Phys. J. Spec. Top.

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We implement several symplectic integrators, which are based on two part splitting, for studying the chaotic behavior of one-and two-dimensional disordered Klein-Gordon lattices with many degrees of freedom and investigate their numerical performance. For this purpose, we perform extensive numerical simulations by considering many different initial energy excitations and following the evolution of the created wave packets in the various dynamical regimes exhibited by these models. We compare the efficiency of the considered integrators by checking their ability to correctly reproduce several features of the wave packets propagation, like the characteristics of the created energy distribution and the time evolution of the systems' maximum Lyapunov exponent estimator. Among the tested integrators the fourth order ABA864 scheme [59] showed the best performance as it needed the least CPU time for capturing the correct dynamical behavior of all considered cases when a moderate accuracy in conserving the systems' total energy value was required. Among the higher order schemes used to achieve a better accuracy in the energy conservation, the sixth order scheme s11ABA82 6 exhibited the best performance.

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“…Numerous studies have considered 'uniform' (i.e., monoatomic) one-dimensional (1D) lattices, which are chains in which each particle in the lattice is identical. However, particles need not be identical, and examinations of such 'heterogenous' lattices [51], with either periodic [43,44,65,79] or random [32,54] distributions of different particles, reveal a wealth of fascinating dynamics that do not arise in uniform lattices. Such dynamics include new families of solitary waves that have been observed in diatomic granular chains and which can exist only for discrete values of the ratio between the masses of the two particles in a diatomic unit [43].…”

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confidence: 99%

Nanoptera in a Period-2 Toda Chain

Lustri¹,

Porter²

2018

SIAM J. Appl. Dyn. Syst.

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We study asymptotic solutions to a singularly-perturbed, period-2 Toda lattice and use exponential asymptotics to examine 'nanoptera', which are nonlocal solitary waves with constant-amplitude, exponentially small wave trains. With this approach, we isolate the exponentially small, constant-amplitude waves, and we elucidate the dynamics of these waves in terms of the Stokes phenomenon. We find a simple asymptotic expression for the waves, and we study configurations in which these waves vanish, producing localized solitary-wave solutions. In the limit of small mass ratio, we derive a simple anti-resonance condition for the manifestation these wave-free solutions.

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Nonlinear lattice waves in heterogeneous media

Cited by 64 publications

References 123 publications

Characteristics of chaos evolution in one-dimensional disordered nonlinear lattices

Characteristics of chaos evolution in one-dimensional disordered nonlinear lattices

Computational efficiency of symplectic integration schemes: application to multidimensional disordered Klein–Gordon lattices

Nanoptera in a Period-2 Toda Chain

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