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Collision-induced amplitude dynamics of fast 2D solitons in the presence of the generic nonlinear loss 一般非线性损耗存在下快速二维孤子的碰撞诱导振幅动力学
arXiv: Pattern Formation and Solitons Pub Date : 2021-03-31 DOI: 10.21203/RS.3.RS-308620/V1
T. Huynh, Nguyen Minh Quan
{"title":"Collision-induced amplitude dynamics of fast 2D solitons in the presence of the generic nonlinear loss","authors":"T. Huynh, Nguyen Minh Quan","doi":"10.21203/RS.3.RS-308620/V1","DOIUrl":"https://doi.org/10.21203/RS.3.RS-308620/V1","url":null,"abstract":"We study the dynamics of two-dimensional (2D) solitons and the fast collisions of two 2D solitons for the nonlinear Schrodinger equations in the presence of the generic weak nonlinear loss. We extend the perturbative technique for calculating the collision-induced dynamics of two one-dimensional (1D) solitons to derive the theoretical expression for the collision-induced amplitude shift in a fast collision of two 2D solitons. Our perturbative approach is based on the standard adiabatic perturbation theory for solitons and the calculations on the energy balance of perturbed solitons due to the generic nonlinear loss. The expression is set up for two types of potentials: the periodic and non-periodic potential. Furthermore, we also present the dependence of the collision-induced amplitude shift on the angle of the two 2D colliding-solitons. Our analytic calculations are confirmed by numerical simulations with the corresponding coupled nonlinear Schrodinger equations in the presence of the cubic loss and in the presence of the quintic loss.","PeriodicalId":154515,"journal":{"name":"arXiv: Pattern Formation and Solitons","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126758714","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: 0
Universality in Phyllotaxis: a Mechanical Theory 叶根趋向性的普遍性:一个力学理论
arXiv: Pattern Formation and Solitons Pub Date : 2021-01-07 DOI: 10.1142/9789814261074_0024
Hyunwoo Lee, L. Levitov
{"title":"Universality in Phyllotaxis: a Mechanical Theory","authors":"Hyunwoo Lee, L. Levitov","doi":"10.1142/9789814261074_0024","DOIUrl":"https://doi.org/10.1142/9789814261074_0024","url":null,"abstract":"One of humanity's earliest mathematical inquiries might have involved the geometric patterns in plants. The arrangement of leaves on a branch, seeds in a sunflower, and spines on a cactus exhibit repeated spirals, which appear with an intriguing regularity providing a simple demonstration of mathematically complex patterns. Surprisingly, the numbers of these spirals are pairs of Fibonacci numbers consecutive in the series 1, 2, 3, 5, 8, 13, 21, 34, 55... obeying a simple rule 1+2=3, 2+3=5, 5+8=13 and so on. This article describes how physics helps to clarify the origin of this fascinating behavior by linking it to the properties of deformable lattices growing and undergoing structural rearrangements under stress.","PeriodicalId":154515,"journal":{"name":"arXiv: Pattern Formation and Solitons","volume":"1774 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129549038","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: 7
Persistence of hydrodynamic envelope solitons: Detection and rogue wave occurrence 水动力包络孤子的持久性:探测和异常波的发生
arXiv: Pattern Formation and Solitons Pub Date : 2020-12-11 DOI: 10.1063/5.0042232
A. Slunyaev
{"title":"Persistence of hydrodynamic envelope solitons: Detection and rogue wave occurrence","authors":"A. Slunyaev","doi":"10.1063/5.0042232","DOIUrl":"https://doi.org/10.1063/5.0042232","url":null,"abstract":"The observation of a wave group persisting for more than 200 periods in the direct numerical simulation of nonlinear unidirectional irregular water waves in deep water is discussed. The simulation conditions are characterized by parameters realistic for broad-banded waves in the sea. The group is identified by the solution of the associated scattering problem for the nonlinear Schrodinger equation as the intense envelope soliton with remarkably stable parameters. Most of extreme waves occur on top of this group, resulting in higher and longer rogue wave events.","PeriodicalId":154515,"journal":{"name":"arXiv: Pattern Formation and Solitons","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127391700","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: 16
Stable and unstable trajectories in a dipolar chain 偶极链中的稳定和不稳定轨迹
arXiv: Pattern Formation and Solitons Pub Date : 2020-12-08 DOI: 10.1103/PhysRevB.103.134443
J. Cisternas, P. Mellado, F. Urbina, Crist'obal Portilla, Miguel Carrasco, A. Concha
{"title":"Stable and unstable trajectories in a dipolar chain","authors":"J. Cisternas, P. Mellado, F. Urbina, Crist'obal Portilla, Miguel Carrasco, A. Concha","doi":"10.1103/PhysRevB.103.134443","DOIUrl":"https://doi.org/10.1103/PhysRevB.103.134443","url":null,"abstract":"In classical mechanics, solutions can be classified according to their stability. Each of them is part of the possible trajectories of the system. However, the signatures of unstable solutions are hard to observe in an experiment, and most of the times if the experimental realization is adiabatic, they are considered just a nuisance. Here we use a small number of XY magnetic dipoles subject to an external magnetic field for studying the origin of their collective magnetic response. Using bifurcation theory we have found all the possible solutions being stable or unstable, and explored how those solutions are naturally connected by points where the symmetries of the system are lost or restored. Unstable solutions that reveal the symmetries of the system are found to be the culprit that shape hysteresis loops in this system. The complexity of the solutions for the nonlinear dynamics is analyzed using the concept of boundary basin entropy, finding that the damping time scale is critical for the emergence of fractal structures in the basins of attraction. Furthermore, we numerically found domain wall solutions that are the smallest possible realizations of transverse walls and vortex walls in magnetism. We experimentally confirmed their existence and stability showing that our system is a suitable platform to study domain wall dynamics at the macroscale.","PeriodicalId":154515,"journal":{"name":"arXiv: Pattern Formation and Solitons","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128011912","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
Modulational instability in a non-Kerr photonic Lieb lattice with metamaterials 具有超材料的非克尔光子Lieb晶格的调制不稳定性
arXiv: Pattern Formation and Solitons Pub Date : 2020-12-08 DOI: 10.1103/PHYSREVA.103.013517
A. K. S. Ali, A. Maimistov, K. Porsezian, A. Govindarajan, M. Lakshmanan
{"title":"Modulational instability in a non-Kerr photonic Lieb lattice with metamaterials","authors":"A. K. S. Ali, A. Maimistov, K. Porsezian, A. Govindarajan, M. Lakshmanan","doi":"10.1103/PHYSREVA.103.013517","DOIUrl":"https://doi.org/10.1103/PHYSREVA.103.013517","url":null,"abstract":"We present an analysis of modulational instability of diffractionless waves in a face-centered square lattice of waveguides featuring non-Kerr nonlinearity, which are constituted by a combination of positive and negative refractive indices. The unit cell of the lattice consists of three different waveguides with different optical properties. The dispersion curve of the lattice supports flat bands and thereby the base equations describing the model have particular solutions that correspond to the diffractionless waves propagating along the waveguides. We also observe a unique ramification of nonlinearities in controlling the flat bands optically. The diffractionless wave solutions are derived and the stability of these distributions are investigated in a nutshell by adopting the standard linear stability approach.","PeriodicalId":154515,"journal":{"name":"arXiv: Pattern Formation and Solitons","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125654105","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: 2
Chimeras on a social-type network 社会类型网络上的嵌合体
arXiv: Pattern Formation and Solitons Pub Date : 2020-11-03 DOI: 10.1051/MMNP/2021012
A. Pikovsky
{"title":"Chimeras on a social-type network","authors":"A. Pikovsky","doi":"10.1051/MMNP/2021012","DOIUrl":"https://doi.org/10.1051/MMNP/2021012","url":null,"abstract":"We consider a social-type network of coupled phase oscillators. Such a network consists of an active core of mutually interacting elements, and of a flock of passive units, which follow the driving from the active elements, but otherwise are not interacting. We consider a ring geometry with a long-range coupling, where active oscillators form a fluctuating chimera pattern. We show that the passive elements are strongly correlated. This is explained by negative transversal Lyapunov exponents.","PeriodicalId":154515,"journal":{"name":"arXiv: Pattern Formation and Solitons","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115384045","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: 8
An introduction to kinks in $varphi^4$-theory $varphi^4$-理论中扭结的介绍
arXiv: Pattern Formation and Solitons Pub Date : 2020-09-01 DOI: 10.21468/SCIPOSTPHYSLECTNOTES.23
Mariya A. Lizunova, J. V. Wezel
{"title":"An introduction to kinks in $varphi^4$-theory","authors":"Mariya A. Lizunova, J. V. Wezel","doi":"10.21468/SCIPOSTPHYSLECTNOTES.23","DOIUrl":"https://doi.org/10.21468/SCIPOSTPHYSLECTNOTES.23","url":null,"abstract":"As a low-energy effective model emerging in disparate fields throughout all of physics, the ubiquitous $varphi^4$-theory is one of the central models of modern theoretical physics. Its topological defects, or kinks, describe stable, particle-like excitations that play a central role in processes ranging from cosmology to particle physics and condensed matter theory. In these lecture notes, we introduce the description of kinks in $varphi^4$-theory and the various physical processes that govern their dynamics. The notes are aimed at advanced undergraduate students, and emphasis is placed on stimulating qualitative insight into the rich phenomenology encountered in kink dynamics. The appendices contain more detailed derivations, and allow enquiring students to also obtain a quantitative understanding. Topics covered include the topological classification of stable solutions, kink collisions, the formation of bions, resonant scattering of kinks, and kink-impurity interactions.","PeriodicalId":154515,"journal":{"name":"arXiv: Pattern Formation and Solitons","volume":"117 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132534546","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: 0
Generalized KdV-type equations versus Boussinesq's equations for uneven bottom -- numerical study. 不均匀底的广义kdv型方程与Boussinesq方程的数值研究。
arXiv: Pattern Formation and Solitons Pub Date : 2020-07-02 DOI: 10.12921/CMST.2020.0000036
A. Karczewska, P. Rozmej
{"title":"Generalized KdV-type equations versus Boussinesq's equations for uneven bottom -- numerical study.","authors":"A. Karczewska, P. Rozmej","doi":"10.12921/CMST.2020.0000036","DOIUrl":"https://doi.org/10.12921/CMST.2020.0000036","url":null,"abstract":"The paper's main goal is to compare the motion of solitary surface waves resulting from two similar but slightly different approaches. In the first approach, the numerical evolution of soliton surface waves moving over the uneven bottom is obtained using single wave equations. In the second approach, the numerical evolution of the same initial conditions is obtained by the solution of a coupled set of the Boussinesq equations for the same Euler equations system. We discuss four physically relevant cases of relationships between small parameters $alpha,beta,delta$. For the flat bottom, these cases imply the Korteweg-de Vries equation (KdV), the extended KdV (KdV2), fifth-order KdV (KdV5), and the Gardner equation (GE). In all studied cases, the influence of the bottom variations on the amplitude and velocity of a surface wave calculated from the Boussinesq equations is substantially more significant than that obtained from single wave equations.","PeriodicalId":154515,"journal":{"name":"arXiv: Pattern Formation and Solitons","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130208651","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
Experimental study of breathers and rogue waves generated by random waves over non-uniform bathymetry 非均匀测深上随机波产生的呼吸波和异常波的实验研究
arXiv: Pattern Formation and Solitons Pub Date : 2020-05-28 DOI: 10.1063/5.0016379
A. Wang, A. Ludu, Z. Zong, L. Zou, Y. Pei
{"title":"Experimental study of breathers and rogue waves generated by random waves over non-uniform bathymetry","authors":"A. Wang, A. Ludu, Z. Zong, L. Zou, Y. Pei","doi":"10.1063/5.0016379","DOIUrl":"https://doi.org/10.1063/5.0016379","url":null,"abstract":"Experimental results describing random, uni-directional, long crested, water waves over non-uniform bathymetry confirm the formation of stable coherent wave packages traveling with almost uniform group velocity. The waves are generated with JONSWAP spectrum for various steepness, height and constant period. A set of statistical procedures were applied to the experimental data, including the space and time variation of kurtosis, skewness, BFI, Fourier and moving Fourier spectra, and probability distribution of wave heights. Stable wave packages formed out of the random field and traveling over shoals, valleys and slopes were compared with exact solutions of the NLS equation resulting in good matches and demonstrating that these packages are very similar to deep water breathers solutions, surviving over the non-uniform bathymetry. We also present events of formation of rogue waves over those regions where the BFI, kurtosis and skewness coefficients have maximal values.","PeriodicalId":154515,"journal":{"name":"arXiv: Pattern Formation and Solitons","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116408768","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: 14
Complex Envelope Variable Approximation in Nonlinear Dynamics 非线性动力学中的复包络变量逼近
arXiv: Pattern Formation and Solitons Pub Date : 2020-04-17 DOI: 10.20537/nd200307
V. Smirnov, L. Manevitch
{"title":"Complex Envelope Variable Approximation in Nonlinear Dynamics","authors":"V. Smirnov, L. Manevitch","doi":"10.20537/nd200307","DOIUrl":"https://doi.org/10.20537/nd200307","url":null,"abstract":"We present the Complex Envelope Variable Approximation (CEVA) as the very useful and compact method for the analysis of the essentially nonlinear dynamical systems. It allows us to study both the stationary and non-stationary dynamics even in the cases, when any small parameters are absent in the initial problem. It is notable that the CEVA admits the analysis of the nonlinear normal modes and their resonant interactions in the discrete systems without any restrictions on the oscillation amplitudes. In this paper we formulate the CEVA's formalism and demonstrate some non-trivial examples of its application. The advantages of the method and possible problems are briefly discussed.","PeriodicalId":154515,"journal":{"name":"arXiv: Pattern Formation and Solitons","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127822325","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: 3
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