Physica D: Nonlinear Phenomena最新文献

{"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}

{"title":"Relativistic effects in the dynamics of a particle in a Coulomb field","authors":"Rafael Ortega ,&nbsp;David Rojas","doi":"10.1016/j.physd.2025.134534","DOIUrl":"10.1016/j.physd.2025.134534","url":null,"abstract":"<div><div>We prove that Bertrand’s property cannot occur in a special-relativistic scenario using the properties of the period function of planar centers. We also explore some integrability properties of the relativistic Coulomb problem and the asymptotic behavior of collision solutions.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"472 ","pages":"Article 134534"},"PeriodicalIF":2.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143163341","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":"Dynamics of nonlinear waves in a low-pass reaction diffusion electrical network and some exact and implicit Modulated compact solutions","authors":"William Kamgaing Mabou ,&nbsp;Désiré Ndjanfang ,&nbsp;Nkeh Oma Nfor ,&nbsp;Muluh Fombu Andrew ,&nbsp;Fabien Kenmogne ,&nbsp;Hatou-Yvelin Donkeng ,&nbsp;David Yemélé","doi":"10.1016/j.physd.2025.134532","DOIUrl":"10.1016/j.physd.2025.134532","url":null,"abstract":"<div><div>In this paper, we analytically investigate the dynamic behavior of the extended nonlinear Schrödinger (ENLS) equation. This equation describes the propagation of the modulated waves in the network characterized by the nonlinear resistance (NLR) by using the rotative waves approximation. Based on the theory of singular systems and investigating the dynamical behavior of the network, we obtain bifurcations of the phase portraits of the system under different parameter conditions. The result of this qualitative investigation indicates the existence of the nonlinear localized waves with linear phase shift, such as bright pulses, peak pulses, dark pulses, compact dark and compact pulses solitary waves. These nonlinear localized waves can be used in signal processing, electronic devices, and ultra-fast metrology. We derive possible exact explicit and implicit solutions propagating in the nonlinear low-pass electrical transmission line with nonlinear dispersion depending on the frequency range of the chosen carrier wave, for physically realistic parameters.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"472 ","pages":"Article 134532"},"PeriodicalIF":2.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143163343","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":"Hamiltonian Lorenz-like models","authors":"Francesco Fedele ,&nbsp;Cristel Chandre ,&nbsp;Martin Horvat ,&nbsp;Nedjeljka Žagar","doi":"10.1016/j.physd.2024.134494","DOIUrl":"10.1016/j.physd.2024.134494","url":null,"abstract":"<div><div>The reduced-complexity models developed by Edward Lorenz are widely used in atmospheric and climate sciences to study nonlinear aspect of dynamics and to demonstrate new methods for numerical weather prediction. A set of inviscid Lorenz models describing the dynamics of a single variable in a zonally-periodic domain, without dissipation and forcing, conserve energy but are not Hamiltonian. In this paper, we start from a general continuous parent fluid model, from which we derive a family of Hamiltonian Lorenz-like models through a symplectic discretization of the associated Poisson bracket, which preserves the Jacobi identity. A symplectic-split integrator is also formulated. These Hamiltonian models conserve energy and maintain the nearest-neighbor couplings inherent in the original Lorenz model. As a corollary, we find that the Lorenz-96 model can be seen as a result of a poor discretization of a Poisson fluid bracket. Hamiltonian Lorenz-like models offer promising alternatives to the original Lorenz models, especially for the qualitative representation of non-Gaussian weather extremes and wave interactions, which underscore many phenomena of the climate system.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"472 ","pages":"Article 134494"},"PeriodicalIF":2.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143162854","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}