Nonlinear Sciences
New submissions
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New submissions for Thu, 23 Nov 17
 [1] arXiv:1711.08220 [pdf, ps, other]

Title: Stabilization of the Peregrine soliton and KuznetsovMa breathers by means of nonlinearity and dispersion managementSubjects: Pattern Formation and Solitons (nlin.PS)
We demonstrate a possibility to make rogue waves (RWs) in the form of the Peregrine soliton (PS) and KuznetsovMa breathers (KMBs) effectively stable objects, with the help of properly defined dispersion or nonlinearity management applied to the continuouswave (CW) background supporting the RWs. In particular, it is found that either management scheme, if applied along the longitudinal coordinate, making the underlying nonlinear Schr\"odinger equation (NLSE) selfdefocusing in the course of disappearance of the PS, indeed stabilizes the global solution with respect to the modulational instability of the background. In the process, additional excitations are generated, namely, dispersive shock waves and, in some cases, also a pair of slowly separating dark solitons. Further, the nonlinearitymanagement format, which makes the NLSE defocusing outside of a finite domain in the transverse direction, enables the stabilization of the KMBs, in the form of confined oscillating states. On the other hand, a nonlinearitymanagement format applied periodically along the propagation direction, creates expanding patterns featuring multiplication of KMBs through their cascading fission.
 [2] arXiv:1711.08252 [pdf, other]

Title: Effect of selfdeflection on a totally asymmetric simple exclusion process with functions of siteassignmentsSubjects: Cellular Automata and Lattice Gases (nlin.CG); Statistical Mechanics (condmat.statmech); Physics and Society (physics.socph)
This study proposes a model of a totally asymmetric simple exclusion process on a single channel lane with functions of siteassignments along the pitlane. The system model attempts to insert a new particle to the leftmost site at a certain probability by randomly selecting one of the empty sites in the pitlane, and reserving it for the particle. Thereafter, the particle is directed to stop at the site only once during its travel. Recently, the system was determined to show a selfdeflection effect, in which the site usage distribution biases spontaneously toward the leftmost site, and the throughput becomes maximum when the site usage distribution is slightly biased to the rightmost site, instead of being an exact uniform distribution. Our exact analysis describes this deflection effect and show a good agreement with simulations.
 [3] arXiv:1711.08395 [pdf, ps, other]

Title: Theory of Heat Equations for Sigma FunctionsComments: 47 pagesSubjects: Exactly Solvable and Integrable Systems (nlin.SI); Algebraic Geometry (math.AG); Number Theory (math.NT)
We consider the heat equations satisfied by the sigma function associated with a planar curve, extending and developing earlier pioneering work of Buchstaber and Leykin. These heat equations lead to useful {\em linear} recursive relations for the coefficients of power series expansion of the sigma function. In particular we exhibit explicit results for curves of genus 3, and give a new constructive proof of an explicit expression for the main matrix in the theory for {\em any} hyperelliptic curve. We also state and prove a new explicit formula for the eigenvalues of the linear operators associated with this matrix, as well as other practical formulae.
 [4] arXiv:1711.08419 [pdf, other]

Title: Nonlocal reductions of the AblowitzLadik equationComments: 20 pages, 1 (png) figure, LaTeXSubjects: Exactly Solvable and Integrable Systems (nlin.SI); Mathematical Physics (mathph); Pattern Formation and Solitons (nlin.PS)
The purpose of the present paper is to develop the inverse scattering transform for the nonlocal semidiscrete nonlinear Schrodinger equation (known as AblowitzLadik equation) with PTsymmetry. This includes: the eigenfunctions (Jost solutions) of the associated Lax pair, the scattering data and the fundamental analytic solutions. In addition, the paper studies the spectral properties of the associated discrete Lax operator. Based on the formulated (additive) RiemannHilbert problem, the 1 and 2soliton solutions for the nonlocal AblowitzLadik equation are derived. Finally, the completeness relation for the associated Jost solutions is proved. Based on this, the expansion formula over the complete set of Jost solutions is derived. This will allow one to interpret the inverse scattering transform as a generalised Fourier transform.
Crosslists for Thu, 23 Nov 17
 [5] arXiv:1708.06323 (crosslist from mathph) [pdf, ps, other]

Title: Quantum groups, YangBaxter maps and quasideterminantsAuthors: Zengo TsuboiComments: 46 pagesJournalref: Nuclear Physics B 926 (2018) 200238Subjects: Mathematical Physics (mathph); High Energy Physics  Theory (hepth); Quantum Algebra (math.QA); Exactly Solvable and Integrable Systems (nlin.SI)
For any quasitriangular Hopf algebra, there exists the universal Rmatrix, which satisfies the YangBaxter equation. It is known that the adjoint action of the universal Rmatrix on the elements of the tensor square of the algebra constitutes a quantum YangBaxter map, which satisfies the settheoretic YangBaxter equation. The map has a zero curvature representation among Loperators defined as images of the universal Rmatrix. We find that the zero curvature representation can be solved by the Gauss decomposition of a product of Loperators. Thereby obtained a quasideterminant expression of the quantum YangBaxter map associated with the quantum algebra $U_{q}(gl(n))$. Moreover, the map is identified with products of quasiPl\"{u}cker coordinates over a matrix composed of the Loperators. We also consider the quasiclassical limit, where the underlying quantum algebra reduces to a Poisson algebra. The quasideterminant expression of the quantum YangBaxter map reduces to ratios of determinants, which give a new expression of a classical YangBaxter map.
 [6] arXiv:1711.07788 (crosslist from hepth) [pdf, other]

Title: Scattering of kinks in a nonpolynomial modelComments: 4 pages, 3 figures; Proceedings of the 3rd International Conference on Particle Physics and Astrophysics, Moscow, 25 October 2017Subjects: High Energy Physics  Theory (hepth); Pattern Formation and Solitons (nlin.PS)
We study a model described by a single real scalar field in the twodimensional spacetime. The model is specified by a potential which is nonpolynomial and supports analytical kinklike solutions that are similar to the standard kinklike solutions that appear in the $\varphi^4$ model when it develops spontaneous symmetry breaking. We investigate the kinkantikink scattering problem in the nonpolynomial model numerically and highlight some specific features, which are not present in the standard case.
 [7] arXiv:1711.08196 (crosslist from quantph) [pdf, other]

Title: Strictly local onedimensional topological quantum error correction with symmetryconstrained cellular automataComments: Submission to SciPostSubjects: Quantum Physics (quantph); Cellular Automata and Lattice Gases (nlin.CG)
Active quantum error correction on topological codes is one of the most promising routes to longterm qubit storage. In view of future applications, the scalability of the used decoding algorithms in physical implementations is crucial. In this work, we focus on the onedimensional Majorana chain and construct a strictly local decoder based on a selfdual cellular automaton. We study numerically and analytically its performance and exploit these results to contrive a scalable decoder with exponentially growing decoherence times in the presence of noise. Our results pave the way for scalable and modular designs of actively corrected onedimensional topological quantum memories.
 [8] arXiv:1711.08318 (crosslist from quantph) [pdf, ps, other]

Title: Local boxcounting dimensions of discrete quantum eigenvalue spectra: Analytical connection to quantum spectral statisticsSubjects: Quantum Physics (quantph); Chaotic Dynamics (nlin.CD)
Two decades ago, Wang and Ong [Phys. Rev. A 55, 1522 (1997)] hypothesized that the local boxcounting dimension of a discrete quantum spectrum should depend exclusively on the nearestneighbor spacing distribution (NNSD) of the spectrum. In this paper, we validate their hypothesis by deriving an explicit formula for the local boxcounting dimension of a countablyinfinite discrete quantum spectrum. This formula expresses the local boxcounting dimension of a spectrum in terms of single and double integrals of the NNSD of the spectrum. As applications, we derive an analytical formula for Poisson spectra and closedform approximations to the local boxcounting dimension for spectra having Gaussian orthogonal ensemble (GOE), Gaussian unitary ensemble (GUE), and Gaussian symplectic ensemble (GSE) spacing statistics. In the Poisson and GOE cases, we compare our theoretical formulas with the published numerical data of Wang and Ong and observe excellent agreement between their data and our theory. We also study numerically the local boxcounting dimensions of the Riemann zeta function zeros and the alternate levels of GOE spectra, which are often used as numerical models of spectra possessing GUE and GSE spacing statistics, respectively. In each case, the corresponding theoretical formula is found to accurately describe the numericallycomputed local boxcounting dimension.
 [9] arXiv:1711.08440 (crosslist from physics.optics) [pdf, ps, other]

Title: Selfadjustment of a nonlinear lasing mode to a pumped area in a twodimensional microcavityComments: 8 pages, 10 figuresJournalref: Photonics Research, Vol. 5, No. 6, pp. B47B53 (2017)Subjects: Optics (physics.optics); Chaotic Dynamics (nlin.CD)
We numerically performed wave dynamical simulations based on the MaxwellBloch (MB) model for a quadrupoledeformed microcavity laser with spatially selective pumping. We demonstrate the appearance of an asymmetric lasing mode whose spatial pattern violates both the x and yaxes mirror symmetries of the cavity. Dynamical simulations revealed that a lasing mode consisting of a clockwise or counterclockwise rotatingwave component is a stable stationary solution of the MB model. From the results of a passivecavity mode analysis, we interpret these asymmetric rotatingwave lasing modes by the locking of four nearly degenerate passivecavity modes. For comparison, we carried out simulations for a uniform pumping case and found a different locking rule for the nearly degenerate modes. Our results demonstrate a nonlinear dynamical mechanism for the formation of a lasing mode that adjusts its pattern to a pumped area.
Replacements for Thu, 23 Nov 17
 [10] arXiv:1212.1710 (replaced) [pdf]

Title: The information and its observer: external and internal information processes, information cooperation, and the origin of the observer intellectAuthors: Vladimir S. LernerComments: 56pages include 15 figuresSubjects: Adaptation and SelfOrganizing Systems (nlin.AO); Information Theory (cs.IT)
 [11] arXiv:1710.10140 (replaced) [pdf, other]

Title: Efficient manifold tracing for planar mapsSubjects: Chaotic Dynamics (nlin.CD); Plasma Physics (physics.plasmph)
 [12] arXiv:1711.02063 (replaced) [pdf, other]

Title: Cluster integrable systems, qPainleve equations and their quantizationComments: 28 pages v.2; 30 pages references added, misprints correctedSubjects: Mathematical Physics (mathph); High Energy Physics  Theory (hepth); Exactly Solvable and Integrable Systems (nlin.SI)
 [13] arXiv:1711.02874 (replaced) [pdf, ps, other]

Title: Excited states of twodimensional solitons supported by the spinorbit coupling and fieldinduced dipoledipole repulsionComments: 8 pages, 3 figures, and 73 referencesSubjects: Quantum Gases (condmat.quantgas); Pattern Formation and Solitons (nlin.PS); Optics (physics.optics)
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