Physica D: Nonlinear Phenomena最新文献

{"title":"Probability distribution in the Toda system: The singular route to a steady state","authors":"Srdjan Petrović ,&nbsp;Nikola Starčević ,&nbsp;Nace Stojanov ,&nbsp;Liang Huang","doi":"10.1016/j.physd.2025.134576","DOIUrl":"10.1016/j.physd.2025.134576","url":null,"abstract":"<div><div>This study reports on the evolution of the probability distribution in the configuration space of the two-dimensional Toda system. The distribution is characterized by singularities, which predominantly take two forms: double-cusped triangular lines and lines parallel to the equipotential line that defines the accessible region. Over time, the number of these singular patterns increases linearly. Consequently, at very large times, the singular patterns fully occupy the accessible area, resulting in a steady state probability distribution with a pronounced singular peak at the center.</div><div>Changes in the singular patterns arise solely from the system's intrinsic dynamics rather than variations in its parameters, emphasizing the system's self-organizing nature over time. These results provide a deeper understanding of the collective motion of particles in symmetric, bounded, two-dimensional conservative systems.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"473 ","pages":"Article 134576"},"PeriodicalIF":2.7,"publicationDate":"2025-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143387312","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Effects of nonlinear coupling parameters on the formation of intrinsic localized modes in a quantum 1D mixed Klein–Gordon/Fermi–Pasta–Ulam chain","authors":"R. Abouem A Ribama ,&nbsp;Z.I. Djoufack ,&nbsp;J.P. Nguenang","doi":"10.1016/j.physd.2025.134556","DOIUrl":"10.1016/j.physd.2025.134556","url":null,"abstract":"<div><div>We analyze the effects of the nonlinear coupling parameters <span><math><msub><mrow><mi>k</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>α</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span> on the formation of intrinsic localized modes (ILMs) in a one-dimensional quantum mixed Klein–Gordon/Fermi–Pasta–Ulam (KG/FPU) chain. Our results indicate that the frequency amplitude is more significantly affected by increasing the values of the nonlinear parameter <span><math><msub><mrow><mi>α</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span> compared to the parameter <span><math><msub><mrow><mi>k</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span>. Additionally, we demonstrate that the mixed system admits breather solutions known as ILMs, with energy exhibiting symmetrical properties. Numerical simulations conducted to support our analytical findings reveal that the <span><math><msub><mrow><mi>k</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span> parameter in the KG potential leads to minimal scattering of phonons, while the <span><math><msub><mrow><mi>α</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span> parameter in the FPU potential results in strong phonon scattering phenomena in the mixed KG/FPU system. Furthermore, we confirm the existence of ILMs through a linear stability analysis, deriving the criteria for the appearance of modulational instability (MI). Our findings show that the shape of MI regions and the instability growth rate are significantly influenced by increases in the nonlinear parameter <span><math><msub><mrow><mi>α</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span>. The theoretical predictions have been validated through numerical tests using the discrete spatial Fourier method, demonstrating full agreement with our analytical results.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"473 ","pages":"Article 134556"},"PeriodicalIF":2.7,"publicationDate":"2025-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143378667","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Nonlinearity mediated miscibility dynamics of mass-imbalanced binary Bose–Einstein condensate for circular atomtronics","authors":"Sriganapathy Raghav ,&nbsp;Suranjana Ghosh ,&nbsp;Barun Halder ,&nbsp;Utpal Roy","doi":"10.1016/j.physd.2025.134558","DOIUrl":"10.1016/j.physd.2025.134558","url":null,"abstract":"<div><div>We explore the nonlinearity-induced and fractional revivals-driven miscibility dynamics of quasi-2D mass-imbalanced binary Bose–Einstein condensates, confined in a ring-shaped waveguide. During their time-evolution, the two condensate species generally remain miscible, as observed in the spatial density distributions and the autocorrelation functions. Although, the investigation is carried out for a wide range of mass-imbalance, initial demonstration is focussed on insignificant mass-imbalance of the two <span><math><mrow><mi>R</mi><mi>b</mi></mrow></math></span>-isotopes with suitable experimental parameters. The characteristic time scales are influenced by the trap parameters and the strengths of nonlinearities. The study also reveals the conditions under which the condensates become spatially distinguishable with clear signatures in their autocorrelation functions. A separability function further identifies favourable parameters and the fractional revival instances for greater separability. We report precise range of the ring-radius and the interaction strength for experimental realization. Additionally, the average separability variation reflects the result across a variety of condensate species.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"474 ","pages":"Article 134558"},"PeriodicalIF":2.7,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143396156","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Rogue wave solutions to the coupled Sasa–Satsuma equation","authors":"Guangxiong Zhang ,&nbsp;Xiyao Chen ,&nbsp;Bao-Feng Feng ,&nbsp;Chengfa Wu","doi":"10.1016/j.physd.2025.134549","DOIUrl":"10.1016/j.physd.2025.134549","url":null,"abstract":"<div><div>In this paper, general rogue wave solutions to the coupled Sasa–Satsuma (CSS) equation are constructed by the Kadomtsev–Petviashvili (KP) reduction method. These rogue wave solutions are classified into three families, which correspond to one complex simple root, two complex simple roots, and one complex double root of an octic algebraic equation related to the dimension reduction condition, respectively. All of these complex roots should have nonzero real and imaginary parts. Furthermore, by considering the case where either only real roots or both real and complex roots of the aforementioned octic algebraic equation are present, other rational solutions such as W-shaped soliton and the mixture of W-shaped soliton and rogue wave solutions to the CSS equation are derived and illustrated.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"474 ","pages":"Article 134549"},"PeriodicalIF":2.7,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143403403","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Influence of coupling symmetries and noise on the critical dynamics of synchronizing oscillator lattices","authors":"Ricardo Gutiérrez,&nbsp;Rodolfo Cuerno","doi":"10.1016/j.physd.2025.134552","DOIUrl":"10.1016/j.physd.2025.134552","url":null,"abstract":"<div><div>Recent work has shown that the synchronization process in lattices of self-sustained (phase and limit-cycle) oscillators displays universal scale-invariant behavior previously studied in the physics of surface kinetic roughening. The type of dynamic scaling ansatz which is verified depends on the randomness that occurs in the system, whether it is columnar disorder (quenched noise given by the random assignment of natural frequencies), leading to anomalous scaling, or else time-dependent noise, inducing the more standard Family-Vicsek dynamic scaling ansatz, as in equilibrium critical dynamics. The specific universality class also depends on the coupling function: for a sine function (as in the celebrated Kuramoto model) the critical behavior is that of the Edwards-Wilkinson equation for the corresponding type of randomness, with Gaussian fluctuations around the average growth. In all the other cases investigated, Tracy–Widom fluctuations ensue, associated with the celebrated Kardar–Parisi–Zhang equation for rough interfaces. Two questions remain to be addressed in order to complete the picture, however: (1) Is the atypical scaling displayed by the sine coupling preserved if other coupling functions satisfying the same (odd) symmetry are employed (as suggested by continuum approximations and symmetry arguments)? and (2) how does the competition between both types of randomness (which are expected to coexist in experimental settings) affect the nonequilibrium behavior? We address the latter question by numerically characterizing the crossover between thermal-noise and columnar-disorder criticality, and the former by providing evidence confirming that it is the symmetry of the coupling function that sets apart the sine coupling, among other odd-symmetric couplings, due to the absence of Kardar–Parisi–Zhang fluctuations.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"473 ","pages":"Article 134552"},"PeriodicalIF":2.7,"publicationDate":"2025-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143372041","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Revisiting viscoelastic liquid films flowing down a slippery substrate: Linear and nonlinear viscoelastic waves","authors":"Zhiwei Song ,&nbsp;Zijing Ding","doi":"10.1016/j.physd.2025.134554","DOIUrl":"10.1016/j.physd.2025.134554","url":null,"abstract":"<div><div>This paper revisits the flow of a viscoelastic film on a slippery substrate (Phys. Rev. Fluids <strong>7</strong> (6), 064007, 2022) using the Navier-slip boundary condition, <span><math><mrow><msub><mrow><mi>τ</mi></mrow><mrow><mi>x</mi><mi>z</mi></mrow></msub><mo>=</mo><mi>λ</mi><mi>u</mi></mrow></math></span> (<span><math><mi>λ</mi></math></span> represents the friction coefficient of the substrate). Here, <span><math><msub><mrow><mi>τ</mi></mrow><mrow><mi>x</mi><mi>z</mi></mrow></msub></math></span> represents the total tangential shear stress, comprised of both a viscous and an elastic component. A model equation for the film thickness is derived based on the long-wave theory. The study investigates both the linear and nonlinear dynamics of the film flow. It reveals that the presence of a slippery substrate and viscoelasticity promote the instability of linear viscoelastic waves. Additionally, they affect the speed and height of nonlinear viscoelastic waves. Our present study suggests that neglecting the elastic component of <span><math><msub><mrow><mi>τ</mi></mrow><mrow><mi>x</mi><mi>z</mi></mrow></msub></math></span> at the slippery wall could result in an overestimation of the linear stability threshold while underestimating the speed and height of nonlinear waves.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"473 ","pages":"Article 134554"},"PeriodicalIF":2.7,"publicationDate":"2025-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143345896","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Garden of bifurcating paths in a nonlinear optical system","authors":"Lucas Sarrazin ,&nbsp;Mathias Marconi ,&nbsp;Massimo Giudici ,&nbsp;Myriam Nonaka ,&nbsp;Monica Agüero ,&nbsp;Alejandro Hnilo ,&nbsp;Marcelo Kovalsky ,&nbsp;Karin Alfaro-Bittner ,&nbsp;Jorge Tredicce","doi":"10.1016/j.physd.2025.134553","DOIUrl":"10.1016/j.physd.2025.134553","url":null,"abstract":"<div><div>We study both theoretically and experimentally the dynamical behavior of a Class B laser with modulated losses. We focus our attention on the response of the system as we sweep the modulation frequency. The nonlinearity of the system introduces a multistability of the laser intensity at resonance but also at subharmonics of the resonance and at harmonics of it. In general subharmonics and harmonics resonances in conjunction with low dissipation are at the origin of multistability in nonlinear dynamical systems. We show the response in intensity for low values of the modulation amplitude. We put in evidence the generation of harmonics of the modulation frequency at subharmonics resonances of the system. The experimental results are in very good agreement with the numerical results obtained from the most simple dynamical model for such type of lasers.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"473 ","pages":"Article 134553"},"PeriodicalIF":2.7,"publicationDate":"2025-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143376742","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Resource-consumer dynamics in drylands: Modeling the role of plant–plant facilitation–competition shifts with a piecewise system","authors":"Leonardo Pereira Costa da Cruz ,&nbsp;Joan Torregrosa ,&nbsp;Miguel Berdugo ,&nbsp;Josep Sardanyés","doi":"10.1016/j.physd.2025.134548","DOIUrl":"10.1016/j.physd.2025.134548","url":null,"abstract":"<div><div>In drylands, water availability determines plant population densities and whether they cooperate via facilitation or compete. When water scarcity intensifies, plant densities decrease and competition for water surpasses the benefits of soil improvement by facilitator plants, involving an abrupt shift from facilitation to competition. Here, we model this facilitation–competition shift using a piecewise system in a resource species such as grasses studying its impact on a resource-consumer dynamical system. First, the dynamics of each system i.e., competitive and cooperative, are introduced separately for this resource-consumer system. The competitive system, by setting conditions to have a monodromic equilibrium in the first quadrant, has no limit cycles. With a monodromy condition in the same quadrant, the cooperative system only has a hyperbolic, small amplitude limit cycle, allowing for an oscillating coexistence. The dynamic properties of the piecewise system become richer. We here prove the extension of the center-focus problem in this particular case, and from a weak focus of order three, we find 3 limit cycles arising from it. We also study the case assuming continuity in the piecewise system. Finally, we present a special and restricted way of obtaining a limit cycle of small amplitude in a pseudo-Hopf bifurcation type. Our results suggest that abrupt density-dependent functional shifts, such as those described in drylands, could introduce novel dynamical phenomena in population dynamis. Our work also provides a novel theoretical framework to model and investigate population dynamics where ecological interactions change due to density-dependent effects.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"473 ","pages":"Article 134548"},"PeriodicalIF":2.7,"publicationDate":"2025-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143372040","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Cubic algebras, induced representations and general solution of the exceptional Laguerre equation X1","authors":"Ian Marquette","doi":"10.1016/j.physd.2025.134547","DOIUrl":"10.1016/j.physd.2025.134547","url":null,"abstract":"<div><div>We consider the case of exceptional Laguerre polynomials <span><math><msub><mrow><mi>X</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> of type I, II and III, their ordinary differential equations and the problem of finding general solutions beside the polynomial part. We will develop an algebraic approach based on the Schrödinger form of the problem and associate representations of the underlying spectrum generating algebra. We use the Darboux–Crum transformation to construct ladder operators of fourth order for the case of the exceptional Laguerre polynomials <span><math><msub><mrow><mi>X</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> of type I, II and III. We then obtain all zero modes for the lowering and raising operators. We construct the induced representation for the linearly independent solutions, including the polynomial states. Those states forming the general solution are important not only in the construction of a wider set of physical states satisfying different boundary conditions but also used in the context of getting isospectral deformations as they allow often to overcome obstruction as several Wronskian constructions of Hamiltonian lead to only formal Darboux transformations. Our approach allows to provide a completely algebraic construction of the two linearly independent solutions of the ordinary differential equation of the exceptional orthogonal polynomials of Laguerre type <span><math><msub><mrow><mi>X</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> ( case I, II and III). The analogues of the Rodrigues formulas for the general solution are constructed. The set of finite states from which the other states can be obtained algebraically is not unique, but the vanishing arrow and diagonal arrow from the diagram of the 2-chain representations can be used to obtain minimal sets. These Rodrigues formulas are then exploited, not only to construct all the states (polynomial and non-polynomial), in a purely algebraic way, but also to obtain coefficients from the action of the ladder operators also in an algebraic manner. Those results are established by means of higher commutation relations related to the cubic Heisenberg–Weyl algebra. The zero modes are associated with eigenstates, but also generalised eigenstates.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"473 ","pages":"Article 134547"},"PeriodicalIF":2.7,"publicationDate":"2025-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143344916","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On non-autonomous Hamiltonian dynamics, dual spaces, and kinetic lifts","authors":"Begüm Ateşli ,&nbsp;Oğul Esen ,&nbsp;Manuel de León ,&nbsp;Cristina Sardón","doi":"10.1016/j.physd.2024.134504","DOIUrl":"10.1016/j.physd.2024.134504","url":null,"abstract":"<div><div>Vlasov kinetic dynamics fits within the Poisson framework, specifically in the Lie–Poisson form. In this context, each particle constituting the plasma follows classical symplectic Hamiltonian motion. More recently, this formulation has been extended to the kinetic formulation of a collection of particles flowing through contact Hamiltonian dynamics.</div><div>In this paper, we introduce geometric kinetic theories within the frameworks of cosymplectic and cocontact manifolds, aiming to generalize the existing literature on symplectic kinetic theory and contact kinetic theory to include time-dependent dynamics. The cosymplectic and cocontact kinetic theories are formulated in terms of both momentum variables and density functions. These alternative realizations are connected through Poisson/momentum maps. Furthermore, in cocontact geometry, we present a hierarchical analysis of nine distinct dynamical motions, which serve as various manifestations of Hamiltonian, evolution, and gradient flows.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"472 ","pages":"Article 134504"},"PeriodicalIF":2.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143163337","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}