Physica D: Nonlinear Phenomena最新文献

{"title":"Magnetic wave dynamics in ferromagnetic thin films: Interactions of solitons and positons in Landau–Lifshitz–Gilbert equation","authors":"Riaz Ur Rahman ,&nbsp;Zaidong Li ,&nbsp;Jingsong He","doi":"10.1016/j.physd.2025.134719","DOIUrl":"10.1016/j.physd.2025.134719","url":null,"abstract":"<div><div>This study explores the higher-order soliton and smooth positon solutions derived from the Landau–Lifshitz–Gilbert (LLG) equation which describes the wave propagation in the physical setting of ferromagnetic thin films by adopting the Darboux transformation (DT) technique. The LLG equation is reformulated into an integrable nonlinear Schrödinger-like equation under the long-wave approximation. This approach facilitates the analysis of the propagation and interaction of magnetic solitons and positons within a ferromagnetic thin films, by taking into account the effects of interfacial Dzyaloshinskii–Moriya (DM) interaction. The DM interaction notably influences the soliton and positon velocities, alters their collision positions, and impacts their propagation trajectories. The magnetization dynamics, described by <span><math><mrow><mover><mrow><mi>m</mi></mrow><mo>→</mo></mover><mo>=</mo><msub><mrow><mi>m</mi></mrow><mrow><mi>x</mi></mrow></msub><msub><mrow><mover><mrow><mi>e</mi></mrow><mo>→</mo></mover></mrow><mrow><mi>x</mi></mrow></msub><mo>+</mo><msub><mrow><mi>m</mi></mrow><mrow><mi>y</mi></mrow></msub><msub><mrow><mover><mrow><mi>e</mi></mrow><mo>→</mo></mover></mrow><mrow><mi>y</mi></mrow></msub><mo>+</mo><msub><mrow><mi>m</mi></mrow><mrow><mi>z</mi></mrow></msub><msub><mrow><mover><mrow><mi>e</mi></mrow><mo>→</mo></mover></mrow><mrow><mi>z</mi></mrow></msub></mrow></math></span>, exhibits distinct characteristics where <span><math><msub><mrow><mi>m</mi></mrow><mrow><mi>x</mi></mrow></msub></math></span> and <span><math><msub><mrow><mi>m</mi></mrow><mrow><mi>y</mi></mrow></msub></math></span> represent oscillations in the plane perpendicular to the external field with breather-like properties, while <span><math><msub><mrow><mi>m</mi></mrow><mrow><mi>z</mi></mrow></msub></math></span> forms localized magnetized states. The magnetization dynamics are characterized through Bloch sphere trajectories, revealing progressively localized spiral patterns for first- and second-order soliton and positon solutions, indicating enhanced spatial confinement of magnetic moments. Moreover, the dynamic behavior of smooth positons within the NLS-type equation is studied using the decomposition method of the modulus square. This methodology offers an approximate characterization of positon trajectories and the time-dependent “phase shift” occurring after collisions.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"479 ","pages":"Article 134719"},"PeriodicalIF":2.7,"publicationDate":"2025-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144116707","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":"Evaluation of probability density function descriptions for three-component Rayleigh–Taylor mixing","authors":"Kevin Ferguson,&nbsp;Brandon E. Morgan","doi":"10.1016/j.physd.2025.134717","DOIUrl":"10.1016/j.physd.2025.134717","url":null,"abstract":"<div><div>Results from simulations of a three-component Rayleigh–Taylor (RT) mixing problem are presented. These simulations are conducted in heavy–light–heavy and heavy–intermediate–light configurations, and each of these configurations are further considered in high- and low-Reynolds-number regimes. This results in RT-unstable flow with one or both interfaces initially unstable, permitting the influence of problem configuration on the statistical description of three-component RT-driven mixing to be considered. Mass fraction covariances are observed to undergo a sign change through the mixing layer in all four configurations considered. This appears to be unique to the multi-component case and represents another way in which multi-component RT mixing differs from the two-component case. Qualitative and quantitative comparisons of joint and marginal probability density function (PDF) descriptions of species concentration are made. Three-, five-, and six-parameter model PDFs are compared against simulation data to assess how accurately they describe the mixing, and it is found that three-component mixing requires at least a five-parameter model PDF to accurately describe the mixing. Notably, the marginal distributions of three-component mixing do not appear to conform to a beta distribution, representing a departure from the classical two-component RT case. Statistical neutrality also appears to influence the optimal choice of model PDF, which is found to be a function of problem configuration.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"479 ","pages":"Article 134717"},"PeriodicalIF":2.7,"publicationDate":"2025-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144107140","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":"On finite-temperature Fredholm determinants","authors":"Oleksandr Gamayun ,&nbsp;Yuri Zhuravlev","doi":"10.1016/j.physd.2025.134716","DOIUrl":"10.1016/j.physd.2025.134716","url":null,"abstract":"<div><div>We consider finite-temperature deformation of the sine kernel Fredholm determinants acting on the closed contours. These types of expressions usually appear as static two-point correlation functions in the models of free fermions and can be equivalently presented in terms of Toeplitz determinants. The corresponding symbol, or the phase shift, is related to the temperature weight. We present an elementary way to obtain large-distance asymptotic behavior even when the phase shift has a non-zero winding number. It is done by deforming the original kernel to the so-called effective form factors kernel that has a completely solvable matrix Riemann–Hilbert problem. This allows us to find explicitly the resolvent and address the subleading corrections. We recover Szegő, Hartwig and Fisher, and Borodin–Okounkov asymptotic formulas.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"479 ","pages":"Article 134716"},"PeriodicalIF":2.7,"publicationDate":"2025-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144107220","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":"Escape by jumps and diffusion by α-stable noise across the barrier in a double well potential","authors":"Ignacio del Amo ,&nbsp;Peter Ditlevsen","doi":"10.1016/j.physd.2025.134709","DOIUrl":"10.1016/j.physd.2025.134709","url":null,"abstract":"<div><div>Many physical and chemical phenomena are governed by stochastic escape across potential barriers. The escape time depends on the structure of the noise and the shape of the potential barrier. By applying <span><math><mi>α</mi></math></span>-stable noise from the <span><math><mrow><mi>α</mi><mo>=</mo><mn>2</mn></mrow></math></span> Gaussian noise limit to the <span><math><mrow><mi>α</mi><mo>&lt;</mo><mn>2</mn></mrow></math></span> jump processes, we find a continuous transition of the mean escape time from the usual dependence on the height of the barrier for Gaussian noise to a dependence solely on the width of the barrier for <span><math><mi>α</mi></math></span>-stable noise. We consider the exit problem of a process driven by <span><math><mi>α</mi></math></span>-stable noise in a double well potential. We study individually the influences of the width and the height of the potential barrier in the escape time, and we show through scalings that the asymptotic laws are described by a universal curve independent of both parameters. When the dependence in the stability parameter is considered, we see that there are two different diffusive regimes in which diffusion is described either by Kramer’s time or by the corresponding asymptotic law for <span><math><mi>α</mi></math></span>-stable noise. We determine the regions of the noise parameter space in which each regime prevails and exploit this result to construct an anomalous example in which a double well potential exhibit a different diffusion regime in each well for a wide range of parameters.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"479 ","pages":"Article 134709"},"PeriodicalIF":2.7,"publicationDate":"2025-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144116705","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":"Relay synchronization and control of dynamics in multiplex networks with unidirectional interlayer coupling","authors":"Aiwin T. Vadakkan ,&nbsp;G. Ambika","doi":"10.1016/j.physd.2025.134715","DOIUrl":"10.1016/j.physd.2025.134715","url":null,"abstract":"<div><div>Multiplex networks provide a proper framework for understanding the dynamics of complex systems with differing types of interactions. This study considers different dynamical states possible in a multiplex network of nonlinear oscillators, with a drive layer and two identical response layers where the interlayer interactions are unidirectional. We report how the directionality in coupling can lead to relay synchronization with amplification in the two response layers through feedback from the middle drive layer. The amplitude of synchronized oscillations of response layers can be controlled by tuning the strength of interlayer coupling. Moreover, we find the synchronization patterns that emerge in the response layers depend on the nature of interlayer coupling, whether feedback or diffusive, and the time scale or parameter mismatches between drive and response layers. Thus, the study indicates the potential for controlling and optimizing the dynamics of response layers remotely by adjusting the strength of interlayer coupling or tuning the dynamic time scale of the drive layer.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"478 ","pages":"Article 134715"},"PeriodicalIF":2.7,"publicationDate":"2025-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144088837","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":"Observability of complex systems via conserved quantities","authors":"Bhargav R. Karamched ,&nbsp;Jack Schmidt ,&nbsp;David Murrugarra","doi":"10.1016/j.physd.2025.134714","DOIUrl":"10.1016/j.physd.2025.134714","url":null,"abstract":"<div><div>Many systems in biology, physics, and engineering are modeled by nonlinear dynamical systems where the states are usually unknown and only a subset of the state variables can be physically measured. Can we understand the full system from what we measure? In the mathematics literature, this question is framed as the observability problem. It has to do with recovering information about the state variables from the observed states (the measurements). In this paper, we relate the observability problem to another structural feature of many models relevant in the physical and biological sciences: the conserved quantity. For models based on systems of differential equations, conserved quantities offer desirable properties such as dimension reduction which simplifies model analysis. Here, we use differential embeddings to show that conserved quantities involving a set of special variables provide more flexibility in what can be measured to address the observability problem for systems of interest in biology. Specifically, we provide conditions under which a collection of conserved quantities make the system observable. We apply our methods to provide alternate measurable variables in models where conserved quantities have been used for model analysis historically in biological contexts.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"477 ","pages":"Article 134714"},"PeriodicalIF":2.7,"publicationDate":"2025-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144072496","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":"Asymmetric dual cascade in gravitational wave turbulence","authors":"Benoît Gay,&nbsp;Sébastien Galtier","doi":"10.1016/j.physd.2025.134712","DOIUrl":"10.1016/j.physd.2025.134712","url":null,"abstract":"<div><div>We numerically simulate, in both the forced and decay regimes, a fourth-order nonlinear diffusion equation derived from the kinetic equation of gravitational wave turbulence in the limit of strongly local quartic interactions. When a forcing is applied to an intermediate wavenumber <span><math><msub><mrow><mi>k</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span>, we observe a dual cascade of energy and wave action. In the stationary state, the associated flux ratio is proportional to <span><math><msub><mrow><mi>k</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span>, and the Kolmogorov–Zakharov spectra are recovered. In decaying turbulence, the study reveals that the wave action spectrum can extend to wavenumbers greater than the initial excitation <span><math><msub><mrow><mi>k</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> with constant negative flux, while the energy flux is positive with a power law dependence in <span><math><mi>k</mi></math></span>. This leads to an unexpected result: a single inertial range with a Kolmogorov–Zakharov wave action spectrum extending progressively to wavenumbers larger than <span><math><msub><mrow><mi>k</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span>. We also observe a wave action decay in time in <span><math><msup><mrow><mi>t</mi></mrow><mrow><mo>−</mo><mn>1</mn><mo>/</mo><mn>3</mn></mrow></msup></math></span> while the front of the energy spectrum progresses according to a <span><math><msup><mrow><mi>t</mi></mrow><mrow><mn>1</mn><mo>/</mo><mn>3</mn></mrow></msup></math></span> law. These properties can be understood with simple theoretical arguments.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"477 ","pages":"Article 134712"},"PeriodicalIF":2.7,"publicationDate":"2025-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144069009","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":"On a high-order shallow-water wave model with canonical non-local Hamiltonian structure","authors":"Christos E. Papoutsellis ,&nbsp;Michel Benoit","doi":"10.1016/j.physd.2025.134691","DOIUrl":"10.1016/j.physd.2025.134691","url":null,"abstract":"<div><div>We derive and study a new family of non-local partial differential equations (PDEs) that model free-surface long gravity waves over a flat bottom. To derive the model equations we approximate the velocity potential as a series of vertical polynomials derived from the shallow-water expansion of the Dirichlet-to-Neumann problem in the Hamiltonian formulation of free-surface potential flow and invoke Luke’s variational principle. The resulting evolution equations exhibit a non-local Hamiltonian structure being coupled with a system of linear elliptic spatial PDEs on the horizontal plane. A key advantage of this approach is that it directly yields canonical Hamiltonian equations, which are well-suited for numerical solutions using standard methods. This class of model equations offers high-order shallow-water approximations of the water-wave problem. It contains terms whose spatial derivatives are at most of order two, distinguishing it from asymptotic methods involving higher-order mixed spatio-temporal derivatives. We explore the first non-trivial member of this family, highlighting its connections to other mathematical models and emphasizing its practical utility. We then analyse and discuss its linear dispersive properties and demonstrate that it does not exhibit a specific type of instability known as wave-trough instability. Additionally, we demonstrate its effectiveness in simulating the long-distance steady propagation of strongly non-linear solitary waves and the head-on collision of two counter-propagating solitary waves. In the latter case, comparisons with experimental data confirm the model’s ability to capture complex wave dynamics, including wave transformation in the presence of strong non-linearity and dispersion. The extension of this approach to accommodate variable bottom topography is briefly discussed.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"479 ","pages":"Article 134691"},"PeriodicalIF":2.7,"publicationDate":"2025-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144107138","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":"Logic with nonlinear maps","authors":"John F. Lindner ,&nbsp;William L. Ditto","doi":"10.1016/j.physd.2025.134710","DOIUrl":"10.1016/j.physd.2025.134710","url":null,"abstract":"<div><div>We demonstrate how to encode boolean functions, including explicit 3, 2, and 1-parameter encodings of <em>all</em> 16 binary boolean functions, in <em>single</em> iterations of unimodal nonlinear maps, which significantly improves previous work. We also demonstrate how multimodal nonlinear maps can simply encode <em>any</em> truth table. A single transistor or diode can realize such unimodal maps electronically and thereby encode diverse logic gates. Open sets of gate parameters protect against errors due to imprecision and noise. These encodings can facilitate the next generation of chaogates, reconfigurable logic gates for secure and efficient dynamics-based computation.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"479 ","pages":"Article 134710"},"PeriodicalIF":2.7,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144107139","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":"The nonlinear steepest descent approach to the long-time asymptotics of the three-coupled Lakshmanan–Porsezian–Daniel model","authors":"Yi Zhao","doi":"10.1016/j.physd.2025.134713","DOIUrl":"10.1016/j.physd.2025.134713","url":null,"abstract":"<div><div>In this paper, the long-time asymptotic behavior of the three-coupled Lakshmanan–Porsezian–Daniel (LPD) model with Schwartz initial data is investigated by the nonlinear steepest descent approach. Based on the Lax pair of the LPD model, a Riemann–Hilbert problem associated with the initial value problem is constructed. Further a sequence of transformations change the Riemann–Hilbert problem into a tractable form via the Deift–Zhou nonlinear steepest descent approach. Then the long-time asymptotics of the LPD model is obtained through reconstruction formula. What distinguishes the 2 × 2 spectral problem is that we treat the matrix in a block form, the advantage of which is that the matrix can be regarded as a block diagonal matrix without being strictly diagonal, necessitating the complexity of the function <span><math><mrow><mi>δ</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></mrow></math></span>. The primary limitation of this approach is that it does not enable direct acquisition of the solution <span><math><mrow><mi>δ</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></mrow></math></span>. To address this challenge, we employ a term involves <span><math><mrow><mi>δ</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow><mo>−</mo><mi>I</mi><mi>⋅</mi><mo>det</mo><mi>δ</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></mrow></math></span>, then the term can be asymptotically estimated as <span><math><mrow><mi>O</mi><mrow><mo>(</mo><msup><mrow><mi>t</mi></mrow><mrow><mo>−</mo><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span>. The distinguishing feature of the long-time asymptotic analysis for our problem, when compared with the nonlinear Schrödinger equation and Hirota equation, lies in the presence of three critical points.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"478 ","pages":"Article 134713"},"PeriodicalIF":2.7,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144088783","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}