Physica D: Nonlinear Phenomena最新文献

{"title":"Bifurcations of unstable eigenvalues for Stokes waves derived from conserved energy","authors":"Sergey Dyachenko ,&nbsp;Dmitry E. Pelinovsky","doi":"10.1016/j.physd.2025.134925","DOIUrl":"10.1016/j.physd.2025.134925","url":null,"abstract":"<div><div>We address Euler’s equations for irrotational gravity waves in an infinitely deep fluid rewritten in conformal variables. Stokes waves are traveling waves with the smooth periodic profiles. In agreement with the previous numerical results, we give a rigorous proof that the zero eigenvalue bifurcation in the linearized equations of motion for co-periodic perturbations occurs at each extremal point of the energy function versus the steepness parameter, provided that the wave speed is not extremal at the same steepness. We derive the leading order of the unstable eigenvalues and, assisted with numerical approximation of its coefficients, we show that the new unstable eigenvalues emerge only in the direction of increasing steepness.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 134925"},"PeriodicalIF":2.9,"publicationDate":"2025-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145020969","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":"Traveling vegetation–herbivore waves may sustain ecosystems threatened by droughts and population growth","authors":"Joydeep Singha ,&nbsp;Hannes Uecker ,&nbsp;Ehud Meron","doi":"10.1016/j.physd.2025.134914","DOIUrl":"10.1016/j.physd.2025.134914","url":null,"abstract":"<div><div>Dryland vegetation can survive water stress by forming spatial patterns but is often subjected to herbivory as an additional stress that puts it at risk of desertification. Understanding the mutual relationships between vegetation patterning and herbivory is crucial for securing food production in drylands, which constitute the majority of rangelands worldwide. Here, we introduce a novel vegetation–herbivore model that captures pattern-forming feedbacks associated with water and herbivory stress and a behavioral aspect of herbivores representing an exploitation strategy. We find that herbivory stress can induce traveling vegetation–herbivore waves and uncover the ecological mechanism that drives their formation. In the traveling-wave state, the herbivore distribution is asymmetric with higher density on one side of each vegetation patch. At low precipitation values their distribution is localized, while at high precipitation the herbivores are spread over the entire landscape. Importantly, their asymmetric distribution results in uneven herbivory stress, strong on one side of each vegetation patch and weak on the opposing side — weaker than the stress exerted in spatially uniform herbivore distribution. Consequently, the formation of traveling waves results in increased sustainability to herbivory stress. We conclude that vegetation–herbivore traveling waves may play an essential role in sustaining herbivore populations under conditions of combined water and herbivory stress, thereby contributing to food security in endangered regions threatened by droughts and population growth.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 134914"},"PeriodicalIF":2.9,"publicationDate":"2025-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145047379","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":"Active Scalar mixing by homogeneous isotropic turbulence","authors":"Joaquim P. Jossy,&nbsp;Pratyush S. Awasthi,&nbsp;Prateek Gupta","doi":"10.1016/j.physd.2025.134926","DOIUrl":"10.1016/j.physd.2025.134926","url":null,"abstract":"<div><div>We study the mixing of active scalars by homogeneous isotropic incompressible stochastic velocity fields. We consider both Navier–Stokes generated turbulent fields as well as synthetically generated homogeneous isotropic stochastic fields. We use Fourier pseudospectral direct numerical simulations to study the mixing dynamics of two non-reacting species of different density ratios. We use the Atwood number to create a denser mixture and a lighter mixture. We show that in the absence of stirring, a denser mixture homogenizes faster than the lighter mixture. The direction of the density gradient causes the interface across which the molecular diffusion occurs to expand outward for the denser blob (lighter mixture) and inward for the lighter blob (denser mixture). The stirring process, which enhances the diffusion process, increases the rate of homogenization in both mixing methods under study. We define a new mixing metric for studying the mixing evolution of active scalars, which indicates that a denser inhomogeneity in a lighter mixture spreads faster but homogenizes slower. For low Mach number turbulence, there is a negligible coupling between the density gradients and the velocity field responsible for stirring. The post-stirring behavior of active scalars is found to be similar to passive scalars, where the scalar energy spectra decay exponentially and exhibit self-similarity. The turbulence fields generated by solving the Navier–Stokes equation homogenize both the mixtures faster than the synthetic cases. We show that matching the kinetic energy spectra and inertial subrange scaling of a synthetically generated stochastic field with that of a Navier–Stokes generated field is not enough to study mixing dynamics.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 134926"},"PeriodicalIF":2.9,"publicationDate":"2025-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145047381","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":"Existence and stability of soliton-based frequency combs in the Lugiato–Lefever equation","authors":"Lukas Bengel,&nbsp;Björn de Rijk","doi":"10.1016/j.physd.2025.134922","DOIUrl":"10.1016/j.physd.2025.134922","url":null,"abstract":"<div><div>Kerr frequency combs are optical signals consisting of a multitude of equally spaced excited modes in frequency space. They are generated in optical microresonators pumped by a continuous-wave laser. It has been experimentally observed that the interplay of Kerr nonlinearity and dispersion in the microresonator can lead to a stable optical signal consisting of a periodic sequence of highly localized ultra-short pulses, resulting in broad frequency spectrum. The discovery that stable broadband frequency combs can be generated in microresonators has unlocked a wide range of promising applications, particularly in optical communications, spectroscopy and frequency metrology. In its simplest form, the physics in the microresonator is modeled by the Lugiato–Lefever equation, a damped nonlinear Schrödinger equation with forcing. In this paper, we rigorously demonstrate that the Lugiato–Lefever equation indeed supports arbitrarily broad Kerr frequency combs by proving the first existence and stability results of periodic solutions consisting of any number of well-separated, strongly localized and highly nonlinear pulses on a single periodicity interval. We realize these periodic multi-soliton solutions as concatenations of individual bright cavity solitons by phrasing the problem as a reversible dynamical system and employing results from homoclinic bifurcation theory. The spatial dynamics formulation enables us to harness general results, based on Evans-function techniques and Lin’s method, to rigorously establish diffusive spectral stability. This, in turn, yields nonlinear stability of the periodic multi-soliton solutions against localized and subharmonic perturbations.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 134922"},"PeriodicalIF":2.9,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145010914","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":"Role of structural properties in reliable prediction of CGLE via data assimilation","authors":"Jing Li ,&nbsp;Tianli Hu","doi":"10.1016/j.physd.2025.134916","DOIUrl":"10.1016/j.physd.2025.134916","url":null,"abstract":"<div><div>The complex Ginzburg–Landau equation (CGLE) is known to exhibit chaotic behavior under certain parametric setups, making long-term prediction challenging due to numerical errors. By leveraging a reference solution obtained from clean numerical simulation (CNS), we compare two different data assimilation strategies using the ensemble Kalman filter (EnKF). Interestingly, the reduced-order model (ROM), despite having larger numerical errors, outperforms the commonly used full-order model (FOM). A detailed analysis reveals that the structural properties of the dynamics play a crucial role in ensuring reliable long-term predictions when the EnKF is applied since the modes of the ROM are particularly effective in preserving these structural properties.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 134916"},"PeriodicalIF":2.9,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145027155","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":"Mathematical modeling on peristaltic flow of a Prandtl fluid with effects of slip conditions and inclined magnetic field","authors":"Sabia Asghar,&nbsp;Fred J. Vermolen","doi":"10.1016/j.physd.2025.134920","DOIUrl":"10.1016/j.physd.2025.134920","url":null,"abstract":"<div><div>The manuscript provides a description of a theoretical analysis of a non-Newtonian Prandtl fluid that is subject to peristaltic flow via an inclined asymmetric channel. We explore the effect of an inclined magnetic field on the peristaltic flow. This is relevant for applications of fluid flow in narrow, inclined (tilted) tubes that are similar to blood vessels or to the digestive system. The model also includes thermodynamic aspects such as heat diffusion (the Soret effect) and viscous dissipation as a result of wall–fluid slip conditions, which help optimize medical devices like lab-on-a-chip systems and dialysis machines. In this study, the concentration of a generic chemical, temperature and fluid velocity are taken into account through mass, heat and momentum balances, respectively. The solution is approximated by the use of numerical techniques that are suitable for cases with long wavelengths (low frequency) and low Reynold’s numbers. The study also discusses the effects of trapping phenomena, which is a crucial issue from a clinical point of view. The developed insights can be used to improve the understanding of physiological flows in the gastrointestinal tract and in blood vessels. By understanding how the fluid moves and how particles are trapped, these insights help to design better medical pumps and artificial organs. A graphical visualization is provided for the fluid velocity profile, temperature distribution and concentration of a generic chemical. Furthermore, a validation of our numerical results has been provided by means of a comparison with a closed-form solution from a benchmark problem. The Prandtl fluid parameters <span><math><mi>α</mi></math></span> and <span><math><mi>β</mi></math></span> have an opposite impact on the axial velocity. Furthermore, an increase in the Schmidt number, <span><math><mrow><mi>S</mi><mi>c</mi></mrow></math></span>, gives a decrease of the concentration of the dissolved chemical. The model predicts that channel inclination has no significant effect on the concentration profile. Furthermore, the model indicates that the Prandtl fluid parameters <span><math><mi>α</mi></math></span> and <span><math><mi>β</mi></math></span> hardly impact the size of the bolus trapped between the streamlines.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 134920"},"PeriodicalIF":2.9,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145020968","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 escape problem and inverse stochastic resonance in a two-dimensional airfoil system driven by fractional Gaussian noise","authors":"Zheng Wang,&nbsp;Jinjie Zhu,&nbsp;Xianbin Liu","doi":"10.1016/j.physd.2025.134919","DOIUrl":"10.1016/j.physd.2025.134919","url":null,"abstract":"<div><div>Aircraft wings encounter complex stochastic loads during flight that traditional Gaussian white noise models inadequately represent. This paper examines a two-dimensional airfoil with nonlinear pitching stiffness subjected to fractional Gaussian noise, employing the Hurst index parameter to simulate the complex random loads experienced by wing structures during flight. Our results reveal significant inverse stochastic resonance, characterized by oscillation suppression at intermediate noise intensities. Anti-persistent noise (<span><math><mrow><mi>H</mi><mo>&lt;</mo><mn>0</mn><mo>.</mo><mn>5</mn></mrow></math></span>) requires higher intensities for optimal suppression while persistent noise (<span><math><mrow><mi>H</mi><mo>&gt;</mo><mn>0</mn><mo>.</mo><mn>5</mn></mrow></math></span>) shows minimal ISR profile variation. To understand the underlying mechanisms of this phenomenon, we conduct escape time analysis between fixed points and limit cycles. Both mean first passage time analysis and probability density functions establish an exponential relationship between transition times and noise intensity that persists across different Hurst indices, despite the non-Markovian nature of the noise. These findings provide valuable insights for airfoil system design in realistic turbulent environments.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"482 ","pages":"Article 134919"},"PeriodicalIF":2.9,"publicationDate":"2025-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144932777","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 competition between wave turbulence and coherent structures","authors":"Benno Rumpf ,&nbsp;Alan C. Newell","doi":"10.1016/j.physd.2025.134923","DOIUrl":"10.1016/j.physd.2025.134923","url":null,"abstract":"<div><div>Wave turbulence of weakly nonlinear dispersive waves is a disordered state in which energy or other conserved quantities are transferred from sources in wavenumber space (the driving range) to sinks (the dissipation range). The theory of wave turbulence provides an analytic derivation of all statistical quantities (most notably the Kolmogorov–Zakharov spectrum) from the underlying equations of motion. A competing and radically different turbulent process with a significant impact on the statistical properties is the formation of coherent structures. Under what conditions can we observe purely weak wave turbulence, and when is it superseded by coherent structures? We study this problem for an influential model of one-dimensional turbulent dynamics, the Majda–McLaughlin–Tabak equation. The formation of narrow radiating solitary waves (pulses) leads to spectra that are steeper than the Kolmogorov–Zakharov spectra. However, for sufficiently large box sizes, we find that wave turbulence prevails within a broad range of four orders of magnitude of the driving force.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 134923"},"PeriodicalIF":2.9,"publicationDate":"2025-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097242","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":"Differential–geometric method of integrating the two-dimensional Heisenberg model","authors":"A.B. Borisov","doi":"10.1016/j.physd.2025.134886","DOIUrl":"10.1016/j.physd.2025.134886","url":null,"abstract":"<div><div>We have integrated the two-dimensional Heisenberg model using classical differential geometry methods. Following a hodograph transformation, the model equations have been stated in terms of a metric tensor and its derivatives in a curvilinear coordinate system. It has been shown that their general solution describes all previously known exact solutions except for a plane vortex. We have predicted and analyzed a new type of vortex structure, a “vortex ring”, in a two-dimensional ferromagnet. Among the latter’s distinctive properties are the limited dimensions of the definition interval, the finiteness of its full energy, and the lack of the vortex core upon the existence of a vortex structure. The present paper covers a two-vortex solution.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"482 ","pages":"Article 134886"},"PeriodicalIF":2.9,"publicationDate":"2025-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144922540","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":"KAN-enhanced deep reinforcement learning for chaos control: Achieving rapid stabilization via minor perturbations","authors":"Tongtao Liu,&nbsp;Yongping Zhang","doi":"10.1016/j.physd.2025.134915","DOIUrl":"10.1016/j.physd.2025.134915","url":null,"abstract":"<div><div>Based on the fact that chaotic systems own dense periodic orbits, chaos control methods represented by the OGY method successfully achieve stabilization with minor control inputs, offering advantages of low energy consumption and non-invasiveness. However, these methods heavily depend on the time required for trajectories to populate chaotic attractors and require prior knowledge of local dynamic information near the target state. These issues hinder their practical applications. In this paper, Kolmogorov–Arnold Networks (KANs) are demonstrated to exhibit significant potential for chaos control via deep reinforcement learning, which is a neural network architecture proposed recently. A new deep reinforcement learning algorithm called parametrized branching dueling Q-network (P-BDQ) is proposed. Then, a new controller is designed based on KANs and P-BDQ. This controller preserves the advantages of the OGY method while reducing the stabilization time through appropriate perturbations applied at each iteration step. Additionally, the data-driven property of deep reinforcement learning avoids the need for explicit modeling of the local system dynamics near a stable state. Numerical simulations demonstrate that this controller performs effectively across multiple chaotic systems.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"482 ","pages":"Article 134915"},"PeriodicalIF":2.9,"publicationDate":"2025-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144932776","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}