Physica D: Nonlinear Phenomena最新文献

{"title":"Novel solitary patterns in a class of Klein–Gordon equations","authors":"Philip Rosenau ,&nbsp;Slava Krylov","doi":"10.1016/j.physd.2025.134640","DOIUrl":"10.1016/j.physd.2025.134640","url":null,"abstract":"<div><div>We study the emergence, stability and evolution of solitons and compactons in a class of Klein–Gordon equations <span><span><span><math><mrow><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi><mi>t</mi></mrow></msub><mo>−</mo><msub><mrow><mi>u</mi></mrow><mrow><mi>x</mi><mi>x</mi></mrow></msub><mo>+</mo><mi>u</mi><mo>=</mo><msup><mrow><mi>u</mi></mrow><mrow><mn>1</mn><mo>+</mo><mi>n</mi></mrow></msup><mo>−</mo><msub><mrow><mi>κ</mi></mrow><mrow><mn>1</mn><mo>+</mo><mn>2</mn><mi>n</mi></mrow></msub><msup><mrow><mi>u</mi></mrow><mrow><mn>1</mn><mo>+</mo><mn>2</mn><mi>n</mi></mrow></msup><mo>,</mo><mspace></mspace><mo>−</mo><mn>1</mn><mo>/</mo><mn>2</mn><mo>&lt;</mo><mi>n</mi><mo>,</mo></mrow></math></span></span></span>endowed with both trivial and non-trivial stable equilibria, and demonstrate that similarly to the classical <span><math><mrow><msub><mrow><mi>κ</mi></mrow><mrow><mn>1</mn><mo>+</mo><mn>2</mn><mi>n</mi></mrow></msub><mo>=</mo><mn>0</mn></mrow></math></span> cases, solitons are linearly unstable, but the instability weakens as <span><math><mrow><msub><mrow><mi>κ</mi></mrow><mrow><mn>1</mn><mo>+</mo><mn>2</mn><mi>n</mi></mrow></msub><mi>↑</mi></mrow></math></span>, and vanishes at <span><math><mrow><msubsup><mrow><mi>κ</mi></mrow><mrow><mn>1</mn><mo>+</mo><mn>2</mn><mi>n</mi></mrow><mrow><mi>c</mi><mi>r</mi><mi>i</mi><mi>t</mi></mrow></msubsup><mo>=</mo><mfrac><mrow><mn>1</mn><mo>+</mo><mi>n</mi></mrow><mrow><msup><mrow><mrow><mo>(</mo><mn>2</mn><mo>+</mo><mi>n</mi><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac></mrow></math></span>, where solitons disappear and kink forms.</div><div>As the growing unstable soliton approaches the non-trivial equilibrium, it morphs into a ’mesaton’, a robust box shaped sharp pulse with a flat-top plateau, which expands at a sonic speed. In the <span><math><msubsup><mrow><mi>κ</mi></mrow><mrow><mn>1</mn><mo>+</mo><mn>2</mn><mi>n</mi></mrow><mrow><mi>c</mi><mi>r</mi><mi>i</mi><mi>t</mi></mrow></msubsup></math></span> vicinity, where instability is suppressed, whereas the internal modes have hardly changed, solitons persist for a very long time but then, rather than turn into mesaton, convert into a breather-like formation.</div><div>Linear damping tempers the conversion and slows mesaton’s propagation. When <span><math><mrow><mo>−</mo><mn>1</mn><mo>/</mo><mn>2</mn><mo>&lt;</mo><mi>n</mi><mo>&lt;</mo><mn>0</mn></mrow></math></span>, compactons emerge and being unstable morph either into a mesaton or into a breather-like formation.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134640"},"PeriodicalIF":2.7,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143724106","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 McMillan mappings I. McMillan multipoles","authors":"Tim Zolkin ,&nbsp;Sergei Nagaitsev ,&nbsp;Ivan Morozov","doi":"10.1016/j.physd.2025.134620","DOIUrl":"10.1016/j.physd.2025.134620","url":null,"abstract":"<div><div>In this article, we consider two dynamical systems: the McMillan sextupole and octupole integrable mappings, originally proposed by Edwin McMillan. Both represent the simplest symmetric McMillan maps, characterized by a single intrinsic parameter. While these systems find numerous applications across various domains of mathematics and physics, some of their dynamical properties remain unexplored. We aim to bridge this gap by providing a comprehensive description of all stable trajectories, including the parametrization of invariant curves, Poincaré rotation numbers, and canonical action–angle variables.</div><div>In the second part, we establish connections between these maps and general chaotic maps in standard form. Our investigation reveals that the McMillan sextupole and octupole serve as first-order approximations of the dynamics around the fixed point, akin to the linear map and quadratic invariant (known as the Courant–Snyder invariant in accelerator physics), which represents zeroth-order approximations (referred to as linearization). Furthermore, we propose a novel formalism for nonlinear Twiss parameters, which accounts for the dependence of rotation number on amplitude. This stands in contrast to conventional betatron phase advance used in accelerator physics, which remains independent of amplitude. Notably, in the context of accelerator physics, this new formalism demonstrates its capability in predicting dynamical aperture around low-order resonances for flat beams, a critical aspect in beam injection/extraction scenarios.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134620"},"PeriodicalIF":2.7,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143716159","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":"Shock waves in an ideal gas with variable density, the radiative and conductive heat fluxes in the presence of gravitational force and magnetic field via the Lie group technique","authors":"Gorakh Nath,&nbsp;Abhay Maurya","doi":"10.1016/j.physd.2025.134637","DOIUrl":"10.1016/j.physd.2025.134637","url":null,"abstract":"<div><div>In our study, we have investigated the spherical (or cylindrical) shock waves propagation in an ideal gas with heat conduction and radiation heat flux in the presence of gravitational force and azimuthal magnetic field via the Lie group transformation technique. In this article, the heat conduction is described using Fourier’s law for heat conduction. In the case of thick gray gas model, the radiation is treated as of the diffusion type. The absorption coefficient and the thermal conductivity are considered to depend on some specific powers of density and temperature. By utilizing the Lie group transformation technique, four potential similarity solution cases were identified, in which the similarity solution exist in only one case (i.e., Case I). In this case, the shock radius follows a power law dependence on time. For this case, the similarity solutions are derived for the flow region behind the shock front, and the impact of problem physical parameters on the flow variables and on the shock strength are studied in detail. The results of this study offer a clear understanding of the influence of radiative and conductive heat transfer parameters, the gravitational parameter, the similarity exponent, and the magnetic field on the shock and on the flow dynamics behind the shock front. It is found that the shock wave decays with an increment in shock Cowling number or the heat transfer parameters or gravitational parameter. On increasing the value of similarity exponent, the strength of the shock wave increases in the non-magnetic case; whereas in the magnetic case, the shock strength reduces. It is also observed that, the shock strength is enhanced, when we change the geometry from cylindrical to spherical.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134637"},"PeriodicalIF":2.7,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143737748","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":"An equation related to the derivative Cahn–Hilliard equation with convection","authors":"Renato Colucci","doi":"10.1016/j.physd.2025.134636","DOIUrl":"10.1016/j.physd.2025.134636","url":null,"abstract":"<div><div>We consider a nonlinear fourth order evolution equation related to the Convective Cahn–Hilliard equation. We study the asymptotic behaviour of the solutions and find the values of the parameters for which solutions converges to the zero steady state and no patterns are observed in the asymptotic behaviour. In other parameter’s regime we obtain the existence of a global attractor. Moreover we prove the existence of periodic travelling waves.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134636"},"PeriodicalIF":2.7,"publicationDate":"2025-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143687954","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":"Data-driven model identification near a supercritical Hopf bifurcation using phase-based approaches","authors":"Dan Wilson","doi":"10.1016/j.physd.2025.134635","DOIUrl":"10.1016/j.physd.2025.134635","url":null,"abstract":"<div><div>A data-driven model identification strategy is developed for dynamical systems near a supercritical Hopf bifurcation with nonautonomous inputs. This strategy draws on phase–amplitude reduction techniques, analytically relating the phase and amplitude response curves to the terms of the controlled Hopf normal form. Fitting can be performed by recording the system output during the relaxation to the stable limit cycle after applying as few as two carefully timed pulse inputs. Unlike standard phase-based model identification strategies, the resulting model is valid in the neighborhood of the Hopf bifurcation, rather than just in a close vicinity of the unperturbed limit cycle. This strategy is illustrated in two examples with relevance to circadian oscillations. In each example, the proposed model identification strategy allows for the formulation, solution, and implementation of a closed loop nonlinear optimal control problem.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134635"},"PeriodicalIF":2.7,"publicationDate":"2025-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143705726","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":"Supercontinuum generation in a few-mode liquid-core fiber","authors":"Lanh Chu Van ,&nbsp;Hieu Le Van ,&nbsp;Van Thuy Hoang","doi":"10.1016/j.physd.2025.134633","DOIUrl":"10.1016/j.physd.2025.134633","url":null,"abstract":"<div><div>Liquid-core fibers have been widely used for supercontinuum generation because of the high nonlinearity and high transparency of selected liquids. These fibers are fabricated using silica capillaries with micrometer core diameters infiltrated with nonlinear liquids. Since nonlinear liquids typically have a refractive index much higher than silica, this results in multimode guidance, especially in large core fibers. This study focuses on numerically investigating supercontinuum generation in a few-mode liquid-core (<span><math><msub><mrow><mtext>CS</mtext></mrow><mrow><mn>2</mn></mrow></msub></math></span>-core) fiber by using a commercial femtosecond laser with a central wavelength of 1560 nm and a pulse duration of 100 fs. The fiber has a core diameter of <span><math><mrow><mn>5</mn><mspace></mspace><mi>μ</mi><mi>m</mi></mrow></math></span> and supports 24 polarized modes. Due to the high noninstantaneous nonlinearity of <span><math><msub><mrow><mtext>CS</mtext></mrow><mrow><mn>2</mn></mrow></msub></math></span>, the liquid-core fiber can achieve supercontinuum generation with higher coherence compared to solid-core fibers, for both linear and circular polarization. Additionally, this work investigates the interaction among the four polarized components of the first high-order mode (<span><math><msub><mrow><mtext>LP</mtext></mrow><mrow><mtext>11</mtext></mrow></msub></math></span>), pointing out the differences in power transfer between the polarized modes in the case of linear and circular polarization. The interaction between <span><math><msub><mrow><mtext>HE</mtext></mrow><mrow><mtext>11,x</mtext></mrow></msub></math></span> and <span><math><msub><mrow><mtext>TM</mtext></mrow><mrow><mtext>01</mtext></mrow></msub></math></span> modes with all existing modes is also discussed.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134633"},"PeriodicalIF":2.7,"publicationDate":"2025-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143680511","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":"Spatiotemporal patterns in a delay-induced infectious disease model with superdiffusion","authors":"Yong Ye,&nbsp;Jin Chen,&nbsp;Yi Zhao","doi":"10.1016/j.physd.2025.134621","DOIUrl":"10.1016/j.physd.2025.134621","url":null,"abstract":"<div><div>Typically, human mobility patterns exhibit distinct large-scale and long-distance features, rendering the standard Brownian motion-based reaction–diffusion modeling inadequate. Consequently, this paper introduces a novel reaction-superdiffusion infectious disease model to delve into the long-distance geographical dissemination of infectious diseases. Theoretically, we have determined the threshold conditions for Turing instability without delay, formulated the amplitude equations characterizing Turing patterns, and devised stability assessment methodologies. Additionally, we have delved into the mechanisms of Hopf and Turing–Hopf bifurcations triggered by delay, utilizing normal form theory and the center manifold theorem to scrutinize the stability and directionality of the resulting periodic solutions. The numerical simulations robustly corroborate the theoretical findings. Notably, while the superdiffusion exponent minimally impacts the pattern shape for Turing patterns, a decrement in its value conspicuously augments the area and isolation of the patches. Conversely, in wave patterns, both the superdiffusion exponent and delay act in concert to modulate the pattern’s morphological evolution. Interestingly, when the selected parameters lie within the Turing–Hopf instability region, we observe spatio-temporal heterogeneous patterns distinct from Turing and spiral patterns. Our findings enrich the existing results.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134621"},"PeriodicalIF":2.7,"publicationDate":"2025-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143680512","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":"Nonlinear dynamics of viscous fingering","authors":"Jack Lawless,&nbsp;Anne Juel,&nbsp;Draga Pihler-Puzović","doi":"10.1016/j.physd.2025.134631","DOIUrl":"10.1016/j.physd.2025.134631","url":null,"abstract":"<div><div>Viscous fingering is an archetype of pattern formation underpinned by a classical hydrodynamic instability, which arises at the interface between a gas bubble displacing viscous fluid in the narrow gap between two parallel plates. Beyond onset, a radially expanding interface develops into highly-branched, continually evolving patterns of fingers. In contrast, an initially flat interface propagating in a rectilinear channel can grow into a steadily advancing symmetric finger, which may in turn destabilise beyond a threshold value of the driving parameter. We approach the complex pattern formation due to viscous fingering from a dynamical systems theory perspective, and discuss the propensity of viscous fingers to exhibit complex dynamics, where the system’s transient evolution corresponds to a meandering between weakly unstable states. We review classical results and examine recent evidence from studies of viscous fingering subjected to controlled perturbations through this lens, thereby providing an alternative perspective on this classical problem, and highlighting open questions.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134631"},"PeriodicalIF":2.7,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143785097","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":"Cross-domain inductive applications with unsupervised (dynamic) Graph Neural Networks (GNN): Leveraging Siamese GNN and energy-based PMI optimization","authors":"Khushnood Abbas ,&nbsp;Shi Dong ,&nbsp;Alireza Abbasi ,&nbsp;Yong Tang","doi":"10.1016/j.physd.2025.134632","DOIUrl":"10.1016/j.physd.2025.134632","url":null,"abstract":"<div><div>The existing body of work in graph embedding has primarily focused on Graph Neural Network (GNN) models designed for transductive settings, meaning these models can only be applied to the specific graph on which they were trained. This limitation restricts the applicability of GNN models, as training them on large graphs is computationally expensive. Additionally, there is a significant research gap in applying these models to cross-domain inductive prediction, where the goal is to train on a smaller graph and generalize to larger or different domain graphs. To address these challenges, this study proposes a novel GNN model capable of generating node representations not only within the same domain but also across different domains. To achieve this, we have explored state-of-the-art Graph Neural Networks (GNNs), including Graph Convolutional Networks, Graph Attention Networks, Graph Isomorphism Networks, and Position-Aware Graph Neural Networks. Furthermore, to effectively learn parameters from smaller graphs, we developed a Siamese Graph Neural Network trained using a novel loss function specifically designed for Graph Siamese Neural Networks. Additionally, to handle real-world sparse graphs efficiently, we provide TensorFlow code optimized for sparse graph operations, significantly reducing spatial complexity. To evaluate the performance of the proposed model, we utilized five real-world dynamic graphs. The model was trained on a smaller dataset in an unsupervised manner, and the pre-trained model was then used to generate both inter- and intra-domain graph node representations. The framework demonstrates robustness, as any state-of-the-art GNN method can be integrated into the Siamese neural network framework to learn parameters using the proposed hybrid cost function. The implementation code is publicly available online to ensure reproducibility of the model: <em>https://github.com/khushnood/UnsupervisedPretrainedCrossdomainInductive NodeRepresentationLearning</em>.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134632"},"PeriodicalIF":2.7,"publicationDate":"2025-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143746558","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":"Rigorous uniaxial limit of the Qian–Sheng inertial Q-tensor hydrodynamics for liquid crystals","authors":"Sirui Li ,&nbsp;Wei Wang ,&nbsp;Qi Zeng","doi":"10.1016/j.physd.2025.134596","DOIUrl":"10.1016/j.physd.2025.134596","url":null,"abstract":"<div><div>This article is concerned with the rigorous connections between the inertial Qian–Sheng model and the Ericksen–Leslie model for the liquid crystal flow, under a more general condition on the coefficients. More specifically, within the framework of Hilbert expansions, we show that: (i) when the elastic coefficients tend to zero (also called the uniaxial limit), the smooth solution to the inertial Qian–Sheng model converges to that to the full inertial Ericksen–Leslie model; (ii) when both the elastic coefficients and the inertial coefficient tend to zero simultaneously, the smooth solution to the inertial Qian–Sheng model converges to that to the noninertial Ericksen–Leslie model.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134596"},"PeriodicalIF":2.7,"publicationDate":"2025-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143680510","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}