arXiv: Pattern Formation and Solitons最新文献_第4页

Stability of gap soliton complexes in the nonlinear Schrödinger equation with periodic potential and repulsive nonlinearity 具有周期势和排斥非线性的非线性Schrödinger方程中间隙孤子复合物的稳定性

arXiv: Pattern Formation and Solitons Pub Date : 2016-11-28 DOI: 10.20537/vm160412

P. P. Kizin

{"title":"Stability of gap soliton complexes in the nonlinear Schrödinger equation with periodic potential and repulsive nonlinearity","authors":"P. P. Kizin","doi":"10.20537/vm160412","DOIUrl":"https://doi.org/10.20537/vm160412","url":null,"abstract":"The work is devoted to numerical investigation of stability of stationary localized modes (\"gap solitons\") for the one-dimentional nonlinear Schr\"odinger equation (NLSE) with periodic potential and repulsive nonlinearity. Two classes of the modes are considered: a bound state of a pair of in-phase and out-of-phase fundamental gap solitons (FGSs) from the first bandgap separated by various number of empty potential wells. Using the standard framework of linear stability analysis, we computed the linear spectra for the gap solitons by means of the Fourier collocation method and the Evans function method. We found that the gap solitons of the first and second classes are exponentially unstable for odd and even numbers of separating periods of the potential, respectively. The real parts of unstable eigenvalues in corresponding spectra decay with the distance between FGSs exponentially. On the contrary, we observed that the modes of the first and second classes are either linearly stable or exhibit weak oscillatory instabilities if the number of empty potential wells separating FGSs is even and odd, respectively. In both cases, the oscillatory instabilities arise in some vicinity of upper bandgap edge. In order to check the linear stability results, we fulfilled numerical simulations for the time-dependent NLSE by means of a finite-difference scheme. As a result, all the considered exponentially unstable solutions have been deformed to long-lived pulsating formations whereas stable solutions conserved their shapes for a long time.","PeriodicalId":154515,"journal":{"name":"arXiv: Pattern Formation and Solitons","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134218851","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Numerical instability of the Akhmediev breather and a finite-gap model of it Akhmediev呼吸机的数值不稳定性及其有限间隙模型

arXiv: Pattern Formation and Solitons Pub Date : 2016-10-31 DOI: 10.1007/978-3-030-04807-5_2

P. Grinevich, P. L. I. F. T. Physics, Russia., Lomonosov Moscow State University, M. Physics, Technology, D. Fisica, Universita di RomaLa Sapienza'', Italy., Istituto Nazionale Fisica Nucleare, Sezione di Roma, 2. Italy.Piazz.leAldoMoro, I-00185 Roma

引用次数: 12

Slanted snaking of localized Faraday waves 局域法拉第波的倾斜蛇形

arXiv: Pattern Formation and Solitons Pub Date : 2016-09-02 DOI: 10.1103/PhysRevFluids.2.064401

Bastián Pradenas, Isidora Araya, M. Clerc, Claudio Falc'on, P. Gandhi, E. Knobloch

引用次数: 13

Aggregation Dynamics Using Phase Wave Signals and Branching Patterns 基于相波信号和分支模式的聚合动力学

arXiv: Pattern Formation and Solitons Pub Date : 2016-07-21 DOI: 10.7566/JPSJ.85.094801

H. Sakaguchi, Takuma Kusagaki

引用次数: 0

Bright solitons in a PT-symmetric chain of dimers pt对称二聚体链中的明亮孤子

arXiv: Pattern Formation and Solitons Pub Date : 2016-07-18 DOI: 10.1155/2016/9514230

O. B. Kirikchi, A. A. Bachtiar, H. Susanto

{"title":"Bright solitons in a PT-symmetric chain of dimers","authors":"O. B. Kirikchi, A. A. Bachtiar, H. Susanto","doi":"10.1155/2016/9514230","DOIUrl":"https://doi.org/10.1155/2016/9514230","url":null,"abstract":"We study the existence and stability of fundamental bright discrete solitons in a parity-time (PT)-symmetric coupler composed by a chain of dimers, that is modelled by linearly coupled discrete nonlinear Schrodinger equations with gain and loss terms. We use a perturbation theory for small coupling between the lattices to perform the analysis, which is then confirmed by numerical calculations. Such analysis is based on the concept of the so-called anti-continuum limit approach. We consider the fundamental onsite and intersite bright solitons. Each solution has symmetric and antisymmetric configurations between the arms. The stability of the solutions is then determined by solving the corresponding eigenvalue problem. We obtain that both symmetric and antisymmetric onsite mode can be stable for small coupling, on the contrary of the reported continuum limit where the antisymmetric solutions are always unstable. The instability is either due to the internal modes crossing the origin or the appearance of a quartet of complex eigenvalues. In general, the gain-loss term can be considered parasitic as it reduces the stability region of the onsite solitons. Additionally, we analyse the dynamic behaviour of the onsite and intersite solitons when unstable, where typically it is either in the form of travelling solitons or soliton blow-ups.","PeriodicalId":154515,"journal":{"name":"arXiv: Pattern Formation and Solitons","volume":"516 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124477836","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 6

Properties of {pi}-mode vibrations in strained carbon chains 应变碳链中{pi}型振动的性质

arXiv: Pattern Formation and Solitons Pub Date : 2016-05-20 DOI: 10.22226/2410-3535-2016-2-146-151

G. Chechin, D. A. Sizintsev, O. Usoltsev

{"title":"Properties of {pi}-mode vibrations in strained carbon chains","authors":"G. Chechin, D. A. Sizintsev, O. Usoltsev","doi":"10.22226/2410-3535-2016-2-146-151","DOIUrl":"https://doi.org/10.22226/2410-3535-2016-2-146-151","url":null,"abstract":"Nonlinear vibrations in strained monoatomic carbon chains are studied with the aid of ab initio methods based on the density functional theory. An unexpected phenomenon of structural transformation at the atomic level above a certain value of the strain was revealed in cumulene chain (carbyne-{beta}). This phenomenon is a consequence of stability loss of the old equilibrium atomic positions that occur at small strain, and appearance of two new stable equilibrium positions near each of them. The aforementioned restructuring gives rise to a softening of {pi}-mode whose frequency tends to zero in a certain region of amplitudes when carbon atoms begin to vibrate near new equilibrium positions. This resembles the concept of soft mode whose \"freezing\" is postulated in the theory of phase transitions in crystals to explain the transitions of displacement type. The dynamical modeling of mass point chains whose particles interact via Lennard-Jones potential can approximate our ab initio results well enough. In particular, this study demonstrates an essential role of dipole-dipole interactions between carbon atoms in formation of their new equilibrium positions in the cumulene chain. We believe that computer studying of Lennard-Jones chains enables to predict properties of various dynamical objects in carbon chains (different nonlinear normal modes and their bushes, discrete breathers etc.) which then can be verified by ab initio methods.","PeriodicalId":154515,"journal":{"name":"arXiv: Pattern Formation and Solitons","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130661664","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 4

Analytical Solutions of Classical and Fractional KP-Burger Equation and Coupled KdV equation 经典和分数阶KP-Burger方程和耦合KdV方程的解析解

arXiv: Pattern Formation and Solitons Pub Date : 2016-02-25 DOI: 10.12921/cmst.2016.0000016

U. Ghosh, S. Sarkar, S. Das

引用次数: 4

Nonlinear vibrational modes in graphene: group-theoretical results 石墨烯中的非线性振动模式:群论结果

arXiv: Pattern Formation and Solitons Pub Date : 2016-01-20 DOI: 10.22226/2410-3535-2016-1-9-15

G. Chechin, D. Ryabov, S. Shcherbinin

引用次数: 22

Frozen Fronts Selection in flow against self-sustained chemical waves 在流动中对抗自我维持的化学波的选择

arXiv: Pattern Formation and Solitons Pub Date : 2015-11-22 DOI: 10.1103/PHYSREVFLUIDS.2.043302

T. Chevalier, D. Salin, L. Talon

引用次数: 6

Exactly solvable Wadati potentials in the PT-symmetric Gross-Pitaevskii equation pt对称Gross-Pitaevskii方程中精确可解的Wadati势

arXiv: Pattern Formation and Solitons Pub Date : 2015-11-20 DOI: 10.1007/978-3-319-31356-6_9

I. V. Barashenkov, D. Zezyulin, V. Konotop

引用次数: 18