# Nonlinear Sciences

## New submissions

[ total of 18 entries: 1-18 ]
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### New submissions for Tue, 20 Mar 18

[1]
Title: On discretization of the Euler top
Authors: A.V. Tsiganov
Comments: 12 pages, 2 figures, LaTeX with AMS fonts
Subjects: Exactly Solvable and Integrable Systems (nlin.SI); Mathematical Physics (math-ph); Dynamical Systems (math.DS)

Application of the intersection theory to construction of n-point finite-difference equations associated with classical integrable systems is discussed. As an example, we present a few new discretizations of motion of the Euler top sharing the integrals of motion with the continuous time system and the Poisson bracket up to the integer scaling factor.

[2]
Title: On weak universality of three-dimensional Larger than Life cellular automaton
Subjects: Cellular Automata and Lattice Gases (nlin.CG)

Larger than Life cellular automaton (LtL) is a class of cellular automata and is a generalization of the game of Life by extending its neighborhood radius. We have studied the three-dimensional extension of LtL. In this paper, we show a radius-4 three-dimensional LtL rule is a candidate for weakly universal one.

[3]
Title: Linear Instability of the Peregrine Breather: Numerical and Analytical Investigations
Comments: 12 pages, 4 figures
Subjects: Exactly Solvable and Integrable Systems (nlin.SI); Mathematical Physics (math-ph)

We study the linear stability of the Peregrine breather both numerically and with analytical arguments based on its derivation as the singular limit of a single-mode spatially periodic breather as the spatial period becomes infinite. By constructing solutions of the linearization of the nonlinear Schr\"odinger equation in terms of quadratic products of components of the eigenfunctions of the Zakharov-Shabat system, we show that the Peregrine breather is linearly unstable. A numerical study employing a highly accurate Chebychev pseudo-spectral integrator confirms exponential growth of random initial perturbations of the Peregrine breather.

[4]
Title: Generalized Hermite polynomials and monodromy-free Schrodinger operators
Comments: 14 pages, 4 figures
Subjects: Exactly Solvable and Integrable Systems (nlin.SI)

We consider a class of monodromy-free \Sch operators with rational potentials constituted by generalized Hermite polynomials. These polynomials defined as Wronskians of classic Hermite polynomials appear in a number of mathematical physics problems as well as in the theory of random matrices and 1D SUSY quantum mechanics. Being quadratic at infinity, those potentials demonstrate localized oscillatory behavior near origin. We derive explicit condition of non-singularity of corresponding potentials and estimate a localization range with respect to indices of polynomials and distribution of their zeros in the complex plane. It turns out that 1D SUSY quantum non-singular potentials come as dressing of harmonic oscillator by polynomial Heisenberg algebra ladder operators. To this end, all generalized Hermite polynomials are produced by appropriate periodic closure of this algebra which leads to rational solutions of Painleve IV equation. We discuss the structure of discrete spectrum of Schrodinger operators and its link to monodromy-free condition.

[5]
Title: Definition and Identification of Information Storage and Processing Capabilities as Possible Markers for Turing-universality in Cellular Automata
Authors: Yanbo Zhang
Comments: 16 pages, 12 figures This paper is accepted by Complex Systems and it will be published soon (vol 27:1)
Subjects: Cellular Automata and Lattice Gases (nlin.CG)

To identify potential universal cellular automata, a method is developed to measure information processing capacity of elementary cellular automata. We consider two features of cellular automata: Ability to store information, and ability to process information. We define local collections of cells as particles of cellular automata and consider information contained by particles. By using this method, information channels and channels' intersections can be shown. By observing these two features, potential universal cellular automata are classified into a certain class, and all elementary cellular automata can be classified into four groups, which correspond to S. Wolfram's four classes: 1) Homogeneous; 2) Regular; 3) Chaotic and 4) Complex. This result shows that using abilities of store and processing information to characterize complex systems is effective and succinct. And it is found that these abilities are capable of quantifying the complexity of systems.

[6]
Title: On the Keldysh Problem of Flutter Suppression
Subjects: Chaotic Dynamics (nlin.CD); Dynamical Systems (math.DS)

This work is devoted to the Keldysh model of flutter suppression and rigorous approaches to its analysis. To solve the stabilization problem in the Keldysh model we use an analog of direct Lyapunov method for differential inclusions. The results obtained here are compared with the results of Keldysh obtained by the method of harmonic balance (describing function method), which is an approximate method for analyzing the existence of periodic solutions. The limitations of the use of describing function method for the study of systems with dry friction and stationary segment are demonstrated.

[7]
Title: Phenomenology of coupled non linear oscillators
Journal-ref: Chaos 28, 023110 (2018)
Subjects: Chaotic Dynamics (nlin.CD)

A recently introduced model of coupled non linear oscillators in a ring is revisited in terms of its information processing capabilities. The use of Lempel-Ziv based entropic measures allows to study thoroughly the complex patterns appearing in the system for different values of the control parameters. Such behaviors, resembling cellular automata, have been characterized both spatially and temporally. Information distance is used to study the stability of the system to perturbations in the initial conditions and in the control parameters. The latter is not an issue in cellular automata theory, where the rules form a numerable set, contrary to the continuous nature of the parameter space in the system studied in this contribution. The variation in the density of the digits, as a function of time is also studied. Local transitions in the control parameter space are also discussed.

[8]
Title: Capturing photoelectron motion with guiding fictitious particles
Comments: Physical Review Letters, American Physical Society, In press
Subjects: Chaotic Dynamics (nlin.CD); Atomic Physics (physics.atom-ph)

Photoelectron momentum distributions (PMDs) from atoms and molecules undergo qualitative changes as laser parameters are varied. We present a model to interpret the shape of the PMDs. The electron's motion is guided by a fictitious particle in our model, clearly characterizing two distinct dynamical behaviors: direct ionization and rescattering. As laser ellipticity is varied, our model reproduces the bifurcation in the PMDs seen in experiments.

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

[9]  arXiv:1803.06372 (cross-list from math.DS) [pdf, other]
Title: Stochastic basins of attraction and generalized committor functions
Subjects: Dynamical Systems (math.DS); Chaotic Dynamics (nlin.CD)

We generalize the concept of basin of attraction of a stable state in order to facilitate the analysis of dynamical systems with noise and to assess stability properties of metastable states and long transients. To this end we examine the notions of mean sojourn times and absorption probabilities for Markov chains and study their convergence to the basin of attraction in the limiting cases. Since any dynamical system described by a transfer operator on a compact domain can be approximated by a Markov chain our approach is applicable to a large variety of problems.

[10]  arXiv:1803.06491 (cross-list from math-ph) [pdf, ps, other]
Title: Solutions of the $U_q(\widehat{\mathfrak{sl}}_N)$ reflection equations
Subjects: Mathematical Physics (math-ph); High Energy Physics - Theory (hep-th); Exactly Solvable and Integrable Systems (nlin.SI)

We find the complete set of invertible solutions of the untwisted and twisted reflection equations for the Bazhanov-Jimbo R-matrix of type ${\mathrm A}^{(1)}_{N-1}$. We also show that all invertible solutions can be obtained by an appropriate affinization procedure from solutions of the constant untwisted and twisted reflection equations.

[11]  arXiv:1803.06527 (cross-list from gr-qc) [pdf, other]
Title: Presence of horizon makes particle motion chaotic
Comments: 5 pages + supplementary material, 6 figures
Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th); Chaotic Dynamics (nlin.CD)

We analyze the motion of a massless particle very near to the event horizon. It reveals that the radial motion has exponential growing nature which is the signature of the presence of chaos in the particle motion. This is being confirmed by investigating the Poincar$\acute{e}$ section of the trajectories with the introduction of a harmonic trap to confine the particle's motion. Two situations are investigated: (a) the black hole is {\it any} static, spherically metric and, (b) spacetime represents a stationary, axisymetric black hole (e.g., Kerr metric). In both cases, the largest Lyapunov exponent has upper bound which is the surface gravity of the horizon. We find that the inclusion of rotation in the spacetime introduces more chaotic fluctuations in the system. The possible implications are finally discussed.

[12]  arXiv:1803.06774 (cross-list from math-ph) [pdf, ps, other]
Title: Toda type equations over multi-dimensional lattices
Subjects: Mathematical Physics (math-ph); Commutative Algebra (math.AC); Exactly Solvable and Integrable Systems (nlin.SI)

We introduce a class of recursions defined over the $d$-dimensional integer lattice. The discrete equations we study are interpreted as higher dimensional extensions to the discrete Toda lattice equation. We shall prove that the equations satisfy the coprimeness property, which is one of integrability detectors analogous to the singularity confinement test. While the degree of their iterates grows exponentially, they exhibit pseudo-integrable nature in terms of the coprimeness property. We also prove that the equations can be expressed as mutations of a seed in the sense of the Laurent phenomenon algebra.

[13]  arXiv:1803.06857 (cross-list from cond-mat.stat-mech) [pdf, other]
Title: Anomalous heat equation in a system connected to thermal reservoirs
Comments: Main text: 5 pages. Supplementary: 9 page. 5 Figures
Subjects: Statistical Mechanics (cond-mat.stat-mech); Mathematical Physics (math-ph); Chaotic Dynamics (nlin.CD)

We study anomalous transport in a one-dimensional system with two conserved quantities in presence of thermal baths. In this system we derive exact expressions of the temperature profile and the two point correlations in steady state as well as in the non-stationary state where the later describes the relaxation to the steady state. In contrast to the Fourier heat equation in the diffusive case, here we show that the evolution of the temperature profile is governed by a non-local anomalous heat equation. We provide numerical verifications of our results.

### Replacements for Tue, 20 Mar 18

[14]  arXiv:1506.00563 (replaced) [pdf, other]
Title: Rational degeneration of M-curves, totally positive Grassmannians and KP2-solitons
Comments: 49 pages, 10 figures. Minor revisions
Subjects: Exactly Solvable and Integrable Systems (nlin.SI); Mathematical Physics (math-ph)
[15]  arXiv:1612.09282 (replaced) [pdf, other]
Title: Interface networks in models of competing alliances
Comments: 7 pages, 8 figures
Subjects: Pattern Formation and Solitons (nlin.PS); Physics and Society (physics.soc-ph)
[16]  arXiv:1701.04903 (replaced) [pdf, other]
Title: The Landau-Lifshitz equation, the NLS, and the magnetic rogue wave as a by-product of two colliding regular "positons"
Comments: 25 pages, 9 figures. Added Section 7 ("7. One last remark: But what of generalization?.."), corrected a number of typos, added 2 more references
Subjects: Exactly Solvable and Integrable Systems (nlin.SI); Materials Science (cond-mat.mtrl-sci)
[17]  arXiv:1704.05276 (replaced) [pdf, other]
Title: Best reply structure and equilibrium convergence in generic games
Comments: Main paper + Supplemental Information
Subjects: Physics and Society (physics.soc-ph); Adaptation and Self-Organizing Systems (nlin.AO); Economics (q-fin.EC)
[18]  arXiv:1708.08568 (replaced) [pdf, other]
Title: How directional mobility affects biodiversity in rock-paper-scissors models
Comments: 6 pages, 10 figures
Subjects: Populations and Evolution (q-bio.PE); Adaptation and Self-Organizing Systems (nlin.AO); Biological Physics (physics.bio-ph)
[ total of 18 entries: 1-18 ]
[ showing up to 2000 entries per page: fewer | more ]

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