# Nonlinear Sciences

## New submissions

[ total of 27 entries: 1-27 ]
[ showing up to 2000 entries per page: fewer | more ]

### New submissions for Tue, 20 Feb 18

[1]
Title: Self-organization on Riemannian manifolds
Subjects: Adaptation and Self-Organizing Systems (nlin.AO); Analysis of PDEs (math.AP); Dynamical Systems (math.DS)

We consider an aggregation model that consists of an active transport equation for the macroscopic population density, where the velocity has a nonlocal functional dependence on the density, modelled via an interaction potential. We set up the model on general Riemannian manifolds and provide a framework for constructing interaction potentials which lead to equilibria that are constant on their supports. We consider such potentials for two specific cases (the two-dimensional sphere and the two-dimensional hyperbolic space) and investigate analytically and numerically the long-time behaviour and equilibrium solutions of the aggregation model on these manifolds.

[2]
Title: Dark-bright soliton pairs: bifurcations and collisions
Subjects: Pattern Formation and Solitons (nlin.PS); Quantum Gases (cond-mat.quant-gas); Atomic Physics (physics.atom-ph); Quantum Physics (quant-ph)

The statics, stability and dynamical properties of dark-bright soliton pairs are investigated motivated by applications in a homogeneous system of two-component repulsively interacting Bose-Einstein condensate. One of the intra-species interaction coefficients is used as the relevant parameter controlling the deviation from the integrable Manakov limit. Two different families of stationary states are identified consisting of dark-bright solitons that are either anti-symmetric (out-of-phase) or asymmetric (mass imbalanced) with respect to their bright soliton. Both of the above dark-bright configurations coexist at the integrable limit of equal intra- and inter-species repulsions and are degenerate in that limit. However, they are found to bifurcate from it in a transcritical bifurcation. The latter interchanges the stability properties of the bound dark-bright pairs rendering the anti-symmetric states unstable and the asymmetric ones stable past the associated critical point (and vice versa before it). Finally, on the dynamical side, it is found that large kinetic energies and thus rapid soliton collisions are essentially unaffected by the intra-species variation, while cases involving near equilibrium states or breathing dynamics are significantly modified under such a variation.

[3]
Title: A note on the integrability of Hamiltonian 1 : 2 : 2 resonance
Authors: Ognyan Christov
Subjects: Exactly Solvable and Integrable Systems (nlin.SI)

We study the integrability of the Hamiltonian normal form of 1 : 2 : 2 resonance. It is known that this normal form truncated to order three is integrable. The truncated to order four normal form contains too many parameters. For a generic choice of parameters in the normal form up to order four we prove a non-integrability result using Morales-Ramis theory. We also isolate a non-trivial case of integrability.

[4]
Title: Direct linearisation of the discrete-time two-dimensional Toda lattices
Authors: Wei Fu
Subjects: Exactly Solvable and Integrable Systems (nlin.SI); Mathematical Physics (math-ph)

The discrete-time two-dimensional Toda lattice of $A_\infty$-type is studied within the direct linearisation framework, which allows us to deal with several nonlinear equations in this class simultaneously and to construct more general solutions of these equations. The periodic reductions of this model are also considered, giving rise to the discrete-time two-dimensional Toda lattices of $A_{r-1}^{(1)}$-type for $r\geq 2$ together with their integrable structures. Particularly, the $A_{r-1}^{(1)}$ classes cover some of the discrete integrable systems very recently found by Fordy and Xenitidis [J. Phys. A: Math. Theor. 50 (2017) 165205], which amount to the negative flows of members in the discrete Gel'fand-Dikii hierarchy.

[5]
Title: Solitons and rogue waves in spinor Bose-Einstein condensates
Comments: 19 pages, 10 figures, 3 tables, to appear in Phys. Rev. E
Subjects: Exactly Solvable and Integrable Systems (nlin.SI)

We present a general classification of one-soliton solutions as well as novel families of rogue-wave solutions for $F=1$ spinor Bose-Einstein condensates (BECs). These solutions are obtained from the inverse scattering transform for a focusing matrix nonlinear Schr\"odinger equation which models condensates in the case of attractive mean field interactions and ferromagnetic spin-exchange interactions. In particular, we show that, when no background is present, all one-soliton solutions are reducible via unitary transformations to a combination of oppositely-polarized solitonic solutions of single-component BECs. On the other hand, we show that, when a non-zero background is present, not all matrix one-soliton solutions are reducible to a simple combination of scalar solutions. We show that some solitons are topological ones and others are dark-bright solitons. Finally, by taking suitable limits of all the solutions on a non-zero background we also obtain three families of rogue-wave (i.e., rational) solutions, two of which are novel to the best of our knowledge.

[6]
Title: Classical Lie symmetries and reductions for a generalized NLS equation in 2+1 dimensions
Journal-ref: Journal of Nonlinear Mathematical Physics, 24: Sup1 (2017) 48-60
Subjects: Exactly Solvable and Integrable Systems (nlin.SI)

A non-isospectral linear problem for an integrable 2+1 generalization of the non linear Schr\"odinger equation, which includes dispersive terms of third and fourth order, is presented. The classical symmetries of the Lax pair and the related reductions are carefully studied. We obtain several reductions of the Lax pair that yield in some cases non-isospectral problems in 1+1 dimensions.

[7]
Title: Emission of autoresonant trajectories and thresholds of resonant pumping
Authors: O.M. Kiselev
Subjects: Chaotic Dynamics (nlin.CD); Mathematical Physics (math-ph); Dynamical Systems (math.DS)

We study an autoresonant asymptotic behaviour for nonlinear oscillators under slowly changing frequency and amplitude of external driver. As a result we obtain formulas for threshold values of amplitude and frequency of the driver when autoresonant behaviour for the nonlinear oscillator is observed. Also we study a capture into resonance and emission out of the resonance for trajectories of the oscillator. A measure of autoresonant asymptotic behaviours for nonlinear oscillator is obtained.

### Cross-lists for Tue, 20 Feb 18

[8]  arXiv:1802.05890 (cross-list from hep-th) [pdf, ps, other]
Title: LeClair-Mussardo series for two-point functions in Integrable QFT
Subjects: High Energy Physics - Theory (hep-th); Statistical Mechanics (cond-mat.stat-mech); Exactly Solvable and Integrable Systems (nlin.SI)

We develop a well-defined spectral representation for two-point functions in relativistic Integrable QFT in finite density situations, valid for space-like separations. The resulting integral series is based on the infinite volume, zero density form factors of the theory, and certain statistical functions related to the distribution of Bethe roots in the finite density background. Our final formulas are checked by comparing them to previous partial results obtained in a low-temperature expansion. It is also show that in the limit of large separations the new integral series factorizes into the product of two LeClair-Mussardo series for one-point functions, thereby satisfying the clustering requirement for the two-point function.

[9]  arXiv:1802.06233 (cross-list from physics.optics) [pdf, other]
Title: Persistence and Stochastic Periodicity in the Intensity Dynamics of a Fiber Laser During the Transition to Optical Turbulence
Subjects: Optics (physics.optics); Chaotic Dynamics (nlin.CD)

Many natural systems display transitions among different dynamical regimes, which are difficult to identify when the data is noisy and high dimensional. A technologically relevant example is a fiber laser, which can display complex dynamical behaviors that involve nonlinear interactions of millions of cavity modes. Here we study the laminar-turbulence transition that occurs when the laser pump power is increased. By applying various data analysis tools to empirical intensity time series we characterize their persistence and demonstrate that at the transition temporal correlations can be precisely represented by a surprisingly simple model.

[10]  arXiv:1802.06364 (cross-list from math.DS) [pdf, other]
Title: The total variation of invariant graphs in forced systems
Subjects: Dynamical Systems (math.DS); Chaotic Dynamics (nlin.CD)

In skew-product systems with contractive factors, all orbits asymptotically approach the graph of the so-called sync function; hence, the corresponding regularity properties primarily matter. In the literature, sync function Lipschitz continuity and differentiability have been proved to hold depending on the derivative of the base reciprocal, if not on its Lyapunov exponent. However, forcing topological features can also impact the sync function regularity. Here, we estimate the total variation of sync functions generated by one-dimensional Markov maps. A sharp condition for bounded variation is obtained depending on parameters, that involves the Markov map topological entropy. The results are illustrated with examples.

[11]  arXiv:1802.06410 (cross-list from math.AP) [pdf, other]
Title: Emergence of oscillatory behaviors for excitable systems with noise and mean-field interaction, a slow-fast dynamics approach
Subjects: Analysis of PDEs (math.AP); Mathematical Physics (math-ph); Dynamical Systems (math.DS); Probability (math.PR); Adaptation and Self-Organizing Systems (nlin.AO)

We consider the long-time dynamics of a general class of nonlinear Fokker-Planck equations, describing the large population behavior of mean-field interacting units. The main motivation of this work concerns the case where the individual dynamics is excitable, i.e. when each isolated dynamics rests in a stable state, whereas a sufficiently strong perturbation induces a large excursion in the phase space. We address the question of the emergence of oscillatory behaviors induced by noise and interaction in such systems. We tackle this problem by considering this model as a slow-fast system (the mean value of the process giving the slow dynamics) in the regime of small individual dynamics and by proving the existence of a positively stable invariant manifold, whose slow dynamics is at first order the dynamics of a single individual averaged with a Gaussian kernel. We consider applications of this result to Stuart-Landau and FitzHugh-Nagumo oscillators.

[12]  arXiv:1802.06580 (cross-list from cond-mat.dis-nn) [pdf, other]
Title: Oscillation death induced by time-varying network
Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn); Statistical Mechanics (cond-mat.stat-mech); Pattern Formation and Solitons (nlin.PS); Physics and Society (physics.soc-ph); Neurons and Cognition (q-bio.NC)

The synchronous dynamics of an array of excitable oscillators, coupled via a generic graph, is studied. Non homogeneous perturbations can grow and destroy synchrony, via a self-consistent instability which is solely instigated by the intrinsic network dynamics. By acting on the characteristic time-scale of the network modulation, one can make the examined system to behave as its (partially) averaged analog. This result if formally obtained by proving an extended version of the averaging theorem, which allows for partial averages to be carried out. Oscillation death are reported to follow the onset of the network driven instability.

[13]  arXiv:1802.06582 (cross-list from math.DG) [pdf, ps, other]
Title: Algebraic non-integrability of magnetic billiards on the Sphere and Hyperbolic plane
Subjects: Differential Geometry (math.DG); Dynamical Systems (math.DS); Exactly Solvable and Integrable Systems (nlin.SI)

We consider billiard ball motion in a convex domain on a constant curvature surface influenced by the constant magnetic field. We examine the existence of integral of motion which is polynomial in velocities. We prove that if such an integral exists then the boundary curve of the domain determines an algebraic curve in $\mathbf{C}^3$ which must be nonsingular. Using this fact we deduce that for any domain different from round disc for all but finitely many values of the magnitude of the magnetic field billiard motion does not have Polynomial in velocities integral of motion.

[14]  arXiv:1802.06635 (cross-list from physics.optics) [pdf]
Title: Optical tristability and ultrafast Fano switching in nonlinear magneto-plasmonic nanoparticles
Subjects: Optics (physics.optics); Adaptation and Self-Organizing Systems (nlin.AO)

We consider light scattering by a coated magneto-plasmonic nanoparticle (MPNP) with a Kerr-type nonlinear plasmonic shell and a magneto-optic core. Such structure features two plasmon dipole modes, associated with electronic oscillations on the inner and outer surfaces of the shell. Driven in a nonlinear regime, each mode exhibits a bistable response. Bistability of an inner plasmon leads to switching between this state and a Fano resonance (Fano switching). Once the external light intensity exceeds the critical value, the bistability zones of both eigen modes overlap yielding optical tristability characterized by three stable steady states for a given wavelength and light intensity. We develop a dynamic theory of transitions between nonlinear steady states and estimate the characteristic switching time as short as 0.5 ps. We also show that the magneto-optical (MO) effect allows red- and blue- spectral shift of the Fano profile for right- and left- circular polarizations of the external light, rendering Fano switching sensitive to the light polarization. Specifically, one can reach Fano switching for the right circular polarization while cancelling it for the left circular polarization. Our results point to a novel class of ultrafast Fano switchers tunable by magnetic field for applications in nanophotonics.

### Replacements for Tue, 20 Feb 18

[15]  arXiv:1705.04117 (replaced) [pdf, ps, other]
Title: Bethe Ansatz for two-magnon scattering states in 2D and 3D Heisenberg-Ising ferromagnets
Authors: P. N. Bibikov
Subjects: Strongly Correlated Electrons (cond-mat.str-el); Exactly Solvable and Integrable Systems (nlin.SI)
[16]  arXiv:1707.09247 (replaced) [pdf, other]
Title: Classical and quantum dynamics of a kicked relativistic particle in a box
Journal-ref: Phys.Lett. A, 382, 633 (2018)
Subjects: Quantum Physics (quant-ph); Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Chaotic Dynamics (nlin.CD)
[17]  arXiv:1712.05284 (replaced) [pdf, other]
Title: Adaptation to criticality through organizational invariance in embodied agents
Subjects: Adaptation and Self-Organizing Systems (nlin.AO); Disordered Systems and Neural Networks (cond-mat.dis-nn); Statistical Mechanics (cond-mat.stat-mech); Neural and Evolutionary Computing (cs.NE); Neurons and Cognition (q-bio.NC)
[18]  arXiv:1801.03888 (replaced) [pdf, ps, other]
Title: Synchronization of Two Diffusively Coupled Chaotic Parametrically Excited nonidentical Pendula
Subjects: Adaptation and Self-Organizing Systems (nlin.AO); Pattern Formation and Solitons (nlin.PS)
[19]  arXiv:1511.01238 (replaced) [pdf]
Title: Fast and slow thinking -- of networks: The complementary 'elite' and 'wisdom of crowds' of amino acid, neuronal and social networks
Authors: Peter Csermely
Comments: This a preliminary version of the paper below, please find its illustrative videos here: this http URL
Journal-ref: BioEssays 40, 1700150 (2018)
Subjects: Molecular Networks (q-bio.MN); Disordered Systems and Neural Networks (cond-mat.dis-nn); Social and Information Networks (cs.SI); Adaptation and Self-Organizing Systems (nlin.AO); Biological Physics (physics.bio-ph)
[20]  arXiv:1608.00152 (replaced) [pdf, other]
Title: The mathematics of taffy pullers
Comments: 23 pages, 49 figures, AMSLaTeX with Tikz macros. Contains an extra appendix compared to the published version with some more taffy pullers from the patent literature
Subjects: History and Overview (math.HO); Dynamical Systems (math.DS); Geometric Topology (math.GT); Chaotic Dynamics (nlin.CD)
[21]  arXiv:1609.08769 (replaced) [pdf, ps, other]
Title: A note on the bi-Hamiltonian structure of Coxeter-Toda lattices
Authors: E. Chuño
Subjects: Exactly Solvable and Integrable Systems (nlin.SI)
[22]  arXiv:1703.10767 (replaced) [pdf, other]
Title: Weight of fitness deviation governs strict physical chaos in replicator dynamics
Comments: 13 pages, 3 figures; accepted in Chaos
Subjects: Chaotic Dynamics (nlin.CD); Biological Physics (physics.bio-ph)
[23]  arXiv:1705.10103 (replaced) [pdf, ps, other]
Title: Classical affine W-algebras and the associated integrable Hamiltonian hierarchies for classical Lie algebras
Comments: 57 pages. Minor editing and corrections following the referee suggestions
Subjects: Mathematical Physics (math-ph); Rings and Algebras (math.RA); Representation Theory (math.RT); Exactly Solvable and Integrable Systems (nlin.SI)
[24]  arXiv:1711.09621 (replaced) [pdf, ps, other]
Title: Spontaneous and stimulus-induced coherent states of dynamically balanced neuronal networks
Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn); Statistical Mechanics (cond-mat.stat-mech); Chaotic Dynamics (nlin.CD)
[25]  arXiv:1801.07652 (replaced) [pdf, other]
Title: Vorticity and helicity decompositions and dynamics with Real Schur form of the velocity gradient
Authors: Jian-Zhou Zhu
Comments: quartet resonance analysis is outlined
Subjects: Fluid Dynamics (physics.flu-dyn); Chaotic Dynamics (nlin.CD); Geophysics (physics.geo-ph)
[26]  arXiv:1802.01718 (replaced) [pdf, other]
Title: A Bayesian Nonparametric Approach to Dynamical Noise Reduction
Subjects: Methodology (stat.ME); Chaotic Dynamics (nlin.CD)
[27]  arXiv:1802.04543 (replaced) [pdf, other]
Title: Artin Billiard Exponential Decay of Correlation Functions