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Nonlinear Sciences

New submissions

[ total of 10 entries: 1-10 ]
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New submissions for Thu, 21 Jun 18

[1]  arXiv:1806.07494 [pdf, other]
Title: Resonant Localized Modes in Electrical Lattices with Second Neighbor Coupling
Comments: 9 pages, 10 figures
Subjects: Pattern Formation and Solitons (nlin.PS)

We demonstrate experimentally and corroborate numerically that an electrical lattice with nearest-neighbor and second-neighbor coupling can simultaneously support long-lived coherent structures in the form of both standard intrinsic localized modes (ILMs), as well as resonant ILMs. In the latter case, the wings of the ILM exhibit oscillations due to resonance with a degenerate plane-wave mode. This kind of localized mode has also been termed nanopteron. Here we show experimentally and using realistic simulations of the system that the nanopteron can be stabilized via both direct and subharmonic driving. In the case of excitations at the zone center (i.e., at wavenumber $k=0$), we observed stable ILMs, as well as a periodic localization pattern in certain driving regimes. In the zone boundary case (of wavenumber $k=\pi/a$, where $a$ is the lattice spacing), the ILMs are always resonant with a plane-wave mode, but can nevertheless be stabilized by direct (staggered) and subharmonic driving.

[2]  arXiv:1806.07559 [pdf, ps, other]
Title: Prohibitions caused by nonlocality for Alice-Bob Boussinesq-KdV type systems
Authors: S. Y. Lou
Comments: 16 pages, 5 figures
Subjects: Exactly Solvable and Integrable Systems (nlin.SI); Mathematical Physics (math-ph); Pattern Formation and Solitons (nlin.PS)

It is found that two different celebrate models, the Korteweg de-Vrise (KdV) equation and the Boussinesq equation, are linked to a same model equation but with different nonlocalities. The model equation is called the Alice-Bob KdV (ABKdV) equation which was derived from the usual KdV equation via the so-called consistent correlated bang (CCB) companied by the shifted parity (SP) and delayed time reversal (DTR). The same model can be called as the Alice-Bob Boussinesq (ABB) system if the nonlocality is changed as only one of SP and DTR. For the ABB systems, with help of the bilinear approach and recasting the multi-soliton solutions of the usual Boussinesq equation to an equivalent novel form, the multi-soliton solutions with even numbers and the head on interactions are obtained. However, the multi-soliton solutions with odd numbers and the multi-soliton solutions with even numbers but with pursuant interactions are prohibited. For the ABKdV equation, the multi-soliton solutions exhibit many more structures because an arbitrary odd function of $x+t$ can be introduced as background waves of the usual KdV equation.

[3]  arXiv:1806.07766 [pdf, ps, other]
Title: Resonant behavior and unpredictability in forced chaotic scattering
Subjects: Chaotic Dynamics (nlin.CD)

Chaotic scattering in open Hamiltonian systems is a topic of fundamental interest in physics, which has been mainly studied in the purely conservative case. However, the effect of weak perturbations in this kind of systems has been an important focus of interest in the last decade. In a previous work, the authors studied the effects of a periodic forcing in the decay law of the survival probability, and they characterized the global properties of escape dynamics. In the present paper, we add two important issues in the effects of periodic forcing: the fractal dimension of the set of singularities in the scattering function, and the unpredictability of the exit basins, which is estimated by using the concept of basin entropy. Both the fractal dimension and the basin entropy exhibit a resonant-like decrease as the forcing frequency increases. We provide a theoretical reasoning, which could justify this decreasing in the fractality near the main resonant frequency, that appears for $\omega \approx 1$. We attribute the decrease in the basin entropy to the reduction of the area occupied by the KAM islands and the basin boundaries when the frequency is close to the resonance. Finally, the decay rate of the exponential decay law shows a minimum value of the amplitude, $A_c$, which reflects the complete destruction of the KAM islands in the resonance. We expect that this work could be potentially useful in research fields related to chaotic Hamiltonian pumps, oscillations in chemical reactions and companion galaxies, among others.

Cross-lists for Thu, 21 Jun 18

[4]  arXiv:1806.07529 (cross-list from math.DS) [pdf, ps, other]
Title: Prevalence of Delay Embeddings with a Fixed Observation Function
Subjects: Dynamical Systems (math.DS); Chaotic Dynamics (nlin.CD)

Let $x_{j+1}=\phi(x_{j})$, $x_{j}\in\mathbb{R}^{d}$, be a dynamical system with $\phi$ being a diffeomorphism. Although the state vector $x_{j}$ is often unobservable, the dynamics can be recovered from the delay vector $\left(o(x_{1}),\ldots,o(x_{D})\right)$, where $o$ is the scalar-valued observation function and $D$ is the embedding dimension. The delay map is an embedding for generic $o$, and more strongly, the embedding property is prevalent. We consider the situation where the observation function is fixed at $o=\pi_{1}$, with $\pi_{1}$ being the projection to the first coordinate. However, we allow polynomial perturbations to be applied directly to the diffeomorphism $\phi$, thus mimicking the way dynamical systems are parametrized. We prove that the delay map is an embedding with probability one with respect to the perturbations. Our proof introduces a new technique for proving prevalence using the concept of Lebesgue points.

[5]  arXiv:1806.07730 (cross-list from hep-th) [pdf, other]
Title: Dressed Elliptic String Solutions on RxS^2
Comments: 47 pages, 2 figures
Subjects: High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); Exactly Solvable and Integrable Systems (nlin.SI)

We obtain classical string solutions on RxS^2 by applying the dressing method on string solutions with elliptic Pohlmeyer counterparts. This is realized through the use of the simplest possible dressing factor, which possesses just a pair of poles lying on the unit circle. The latter is equivalent to the action of a single Backlund transformation on the corresponding sine-Gordon solutions. The obtained dressed elliptic strings present an interesting bifurcation of their qualitative characteristics at a specific value of a modulus of the seed solutions. Finally, an interesting generic feature of the dressed strings, which originates from the form of the simplest dressing factor and not from the specific seed solution, is the fact that they can be considered as drawn by an epicycle of constant radius whose center is running on the seed solution. The radius of the epicycle is directly related to the location of the poles of the dressing factor.

Replacements for Thu, 21 Jun 18

[6]  arXiv:1708.01144 (replaced) [pdf, other]
Title: Direct nonlinear Fourier transform algorithms for the computation of solitonic spectra in focusing nonlinear Schrödinger equation
Comments: revised version, submitted to Communication of Nonlinear Science and Numerical Simulations
Subjects: Numerical Analysis (math.NA); Exactly Solvable and Integrable Systems (nlin.SI)
[7]  arXiv:1710.00128 (replaced) [pdf, other]
Title: Delay Embedding of Periodic Orbits Using a Fixed Observation Function
Comments: minor changes
Subjects: Dynamical Systems (math.DS); Chaotic Dynamics (nlin.CD)
[8]  arXiv:1801.05013 (replaced) [pdf, ps, other]
Title: Exact distribution of spacing ratios for random and localized states in quantum chaotic systems
Comments: 10 pages, 6 figures
Journal-ref: Phys. Rev. E 97, 062212 (2018)
Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Chaotic Dynamics (nlin.CD)
[9]  arXiv:1801.09377 (replaced) [pdf, ps, other]
Title: On the validity of linear response theory in high-dimensional deterministic dynamical systems
Comments: 13 pages plus appendices
Subjects: Dynamical Systems (math.DS); Chaotic Dynamics (nlin.CD)
[10]  arXiv:1802.03787 (replaced) [pdf, ps, other]
Title: The continuum limit of the Kuramoto model on sparse random graphs
Subjects: Dynamical Systems (math.DS); Adaptation and Self-Organizing Systems (nlin.AO)
[ total of 10 entries: 1-10 ]
[ showing up to 2000 entries per page: fewer | more ]

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