Physica D: Nonlinear Phenomena最新文献

{"title":"Normal form computation of nonlinear dispersion relationship for locally resonant metamaterial","authors":"Tao Wang ,&nbsp;Cyril Touzé ,&nbsp;Haiqin Li ,&nbsp;Qian Ding","doi":"10.1016/j.physd.2026.135115","DOIUrl":"10.1016/j.physd.2026.135115","url":null,"abstract":"<div><div>This article is devoted to the application of the parametrisation method for invariant manifold with a complex normal form style (CNF), for the derivation of higher-order approximations of underdamped nonlinear dispersion relationships for periodic structures, more specifically by considering the case of a locally resonant metamaterial chain incorporating damping and various nonlinear stiffnesses. Two different strategies are proposed to solve the problem. In the first one, Bloch’s assumption is first applied to the equations of motion. The nonlinear change of coordinates provided by the complex normal form style in the parametrisation method is applied. This direct procedure, which applies first the wave dependency to the original physical coordinates of the problem, is referred to as CNF-BP (for CNF applied with Bloch’s assumption on physical coordinates). In the second strategy, the nonlinear change of coordinates provided by the parametrisation method, which relates the physical coordinates to the so-called normal coordinates, is first applied. Then the periodic assumption is used, thus imposing a Bloch wave ansatz on the normal coordinates. This method will be referred to as CNF-PN (for CNF with a periodic assumption on normal coordinates). In the conservative case, the two CNF calculation strategies are first verified by comparing with the results from existing literature. Subsequently, two carefully selected examples demonstrate that the CNF-PN strategy exhibits superior capability in capturing complex wave propagation phenomena, whereas the CNF-BP strategy encounters limitations in handling non-fundamental harmonics and the nonlinear interactions between host oscillators. The influence of truncation order on the accuracy of CNF-PN is further examined, demonstrating its effectiveness in extending the validity limit. For underdamped systems, the CNF-PN is systematically compared against numerical techniques, a classical analytical perturbation technique (the method of multiple scales), and direct numerical time integration of annular chain structures. The results confirm the exceptional accuracy of the CNF-PN in predicting nonlinear dispersion relationships, damping ratios, invariant manifolds, and wave attenuation characteristics, as long as the validity limit of the asymptotic expansion is not reached. This advancement provides a novel and efficient analytical and numerical tool for studying nonlinear metamaterials.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"488 ","pages":"Article 135115"},"PeriodicalIF":2.9,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038411","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":"Analytic invariant manifolds for Frenkel-Kontorova model with long-range interactions","authors":"Jianguo Si ,&nbsp;Wen Si","doi":"10.1016/j.physd.2026.135111","DOIUrl":"10.1016/j.physd.2026.135111","url":null,"abstract":"<div><div>In this paper, we study the one-dimensional parameterized analytic invariant manifolds (stable, unstable, center and resonant manifolds) of long-range interaction’s Frenkel-Kontorova model, which includes the cases of center and resonant manifolds that are not covered in [1]. The results of this paper formulate a complete theory of analytic invariant manifolds for the above model. We obtain the following results: (1) We prove that the existence of analytic stable or unstable manifolds when eigenvalue does not lie on the unit circle. (2) We prove that the existence of analytic center manifolds when eigenvalue lies on the unit circle but is not a root of unity under the Brjuno condition. (3) We discuss the existence and non-existence of analytic invariant manifolds beyond Brjuno condition. In this case, we first prove the existence of analytic center manifolds when eigenvalue lies on the unit circle and is a root of the unity, which is called the resonance case, and prove that the difference equations may not have a nontrivial center manifold when the Brjuno condition is violated. Finally, we give the numerical simulations for all above cases.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"488 ","pages":"Article 135111"},"PeriodicalIF":2.9,"publicationDate":"2026-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145979129","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":"Wave packet dynamics within the modular Schamel equation","authors":"Marcelo V. Flamarion ,&nbsp;Efim Pelinovsky ,&nbsp;Ekaterina Didenkulova","doi":"10.1016/j.physd.2025.135095","DOIUrl":"10.1016/j.physd.2025.135095","url":null,"abstract":"<div><div>In this article, we investigate the evolution of long waves and the dynamics of wave packets governed by the modular Schamel equation. We show that the wave field disintegrates into solitary waves of both polarities and recurrence is not observed. Their interactions substantially amplify the wave field and, over long times and large domains, can trigger the formation of freak waves. Furthermore, under the assumption of weak nonlinearity, we seek wave packet solutions of the Schamel equation and derive a generalized nonlinear Schrödinger (gNLS) envelope equation, which inherits the same nonlinearity as the Schamel equation. In the parameter regime of interest, the gNLS supports only bright solitons, which inherit the Schamel solitary-wave profile (up to scaling). Additionally, the derived bright soliton was examined as an initial-value problem for the modular Schamel equation, where its numerical stability was confirmed, showing good agreement with the theoretical predictions.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"488 ","pages":"Article 135095"},"PeriodicalIF":2.9,"publicationDate":"2026-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038410","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 near ring solitons of asymmetrical Nizhnik-Novikov-Veselov equation: Integrability and blow-up","authors":"Zheyong Yin ,&nbsp;Xiaofei Zhao","doi":"10.1016/j.physd.2026.135113","DOIUrl":"10.1016/j.physd.2026.135113","url":null,"abstract":"<div><div>This work presents an in-depth analytical and numerical investigation of a special class of ring soliton and dromion solutions to the asymmetrical Nizhnik-Novikov-Veselov (ANNV) equation. We introduce the radius <em>r</em> of the closed curve on which the ring soliton lies to parameterize a family of solutions connecting the ring soliton and the dromion, where <span><math><mrow><mi>r</mi><mo>=</mo><mn>0</mn></mrow></math></span> corresponds to the dromion solution. By fixing the external potential function, we reduced the ANNV equation and analyzed the integrability of the simplified model. Subsequently, we designed a discrete conservation-preserving algorithm to efficiently solve and simulate it. Numerical results verified the conservation and the effectiveness of the algorithm. Furthermore, we explore the rich dynamical behavior of the ring soliton and dromion solutions under various perturbations. Our results show that small perturbations applied to the initial condition can trigger blow-up, and the likelihood of blow-up increases with the radius <em>r</em> of the closed curve.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"488 ","pages":"Article 135113"},"PeriodicalIF":2.9,"publicationDate":"2026-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145979131","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":"Entanglement transformation after 2-localization in ring quantum networks","authors":"Qi Han ,&nbsp;Shijiao Xing ,&nbsp;Xuexin Huang ,&nbsp;Xiao Wu ,&nbsp;Junlin Li","doi":"10.1016/j.physd.2026.135112","DOIUrl":"10.1016/j.physd.2026.135112","url":null,"abstract":"<div><div>Entanglement is a core resource for quantum computing and quantum information, while quantum networks possess complex entanglement structures and constitute the main challenge for realizing quantum technologies. In this paper, we attempt to implement 2-localization in ring quantum networks (RQNs), verify its feasibility, and explore what transformation entanglement undergoes after 2-localization. Specifically, we transform a chaotic Hamiltonian containing high-order multipartite interactions into an isospectral strict 2-local Hamiltonian via unitary transformation and construct a cost function. Performing numerical simulations from multiple perspectives, and we conclude that applying 2-localization in RQNs is feasible. Meanwhile, we consider the degree of entanglement of RQNs before and after 2-localization based on entanglement entropy and concurrence, and eventually find that 2-localization fundamentally changes the entanglement structure of RQNs: the entanglement scaling behavior shifts from volume law to area law. That is, entanglement changes from global genuine multipartite entanglement to localized bipartite entanglement, and entanglement resources are selectively redistributed on specific edges. This discovery provides a new idea for resource optimization in quantum computing and entanglement optimization in quantum networks.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"488 ","pages":"Article 135112"},"PeriodicalIF":2.9,"publicationDate":"2026-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145979130","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 quantum analogs of classical impact oscillators","authors":"Arnab Acharya,&nbsp;Titir Mukherjee,&nbsp;Deepshikha Singh,&nbsp;Soumitro Banerjee","doi":"10.1016/j.physd.2025.135092","DOIUrl":"10.1016/j.physd.2025.135092","url":null,"abstract":"<div><div>This paper investigates the dynamics of quantum analogs of classical impact oscillators to explore how complex nonlinear behaviors manifest in quantum systems. While classical impact oscillators exhibit chaos and bifurcations, quantum systems, governed by linear equations, appear to forbid such dynamics. Through simulations of unforced, forced, and dissipative quantum oscillators, we uncover quasiperiodicity, strange non-chaotic dynamics, and even chaos in the presence of dissipation. Using entropy time series, Fourier spectra, OTOCs, Lyapunov analysis, and the 0–1 test, we demonstrate that quantum systems can exhibit rich dynamical signatures analogous to classical nonlinear systems, bridging quantum mechanics and chaos theory.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"488 ","pages":"Article 135092"},"PeriodicalIF":2.9,"publicationDate":"2026-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145928016","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 deep-atmosphere Euler equations: Explicit solutions and perturbation analysis","authors":"Calin-Iulian Martin","doi":"10.1016/j.physd.2025.135100","DOIUrl":"10.1016/j.physd.2025.135100","url":null,"abstract":"<div><div>We present a method to construct a family of explicit solutions to the deep-atmosphere Euler equations in spherical coordinates. These solutions represent steady purely–azimuthal flows accommodating general stratification that depends on the height and latitude. After prescribing the stratification we derive explicit formulas for the velocity field and for the pressure. From the gas law the temperature is determined explicitly and the heat sources are identified as well from the first law of thermodynamics. By expressing the solution in spherical coordinates, we avoid making any approximations that would simplify the geometry in the governing equations. Following the construction of our explicit solution, we address the suitability of these solutions to describe physically realistic atmospheric flows. By analyzing different choices of the density profile, we demonstrate that the resulting temperature distribution may either decrease (cf. Proposition 1, formula (3.27)) or increase (cf. Proposition 2, formula (3.38)) with height. Both behaviors are physically relevant and correspond to distinct atmospheric regimes. Our study concludes with a short-wavelength stability analysis, revealing that certain flows are stable for a wide range of density distributions that depend on the depth, and on the depth and latitude, respectively.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"488 ","pages":"Article 135100"},"PeriodicalIF":2.9,"publicationDate":"2026-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145928018","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":"Modulational instability, rogue waves and multi-pole solitons for the fifth-order reverse space-time nonlinear Schrödinger equation","authors":"Tianwei Qiu ,&nbsp;Meng’en Wang ,&nbsp;Zhen Wang ,&nbsp;Xue-Ke Liu ,&nbsp;Jiaming Sun","doi":"10.1016/j.physd.2025.135101","DOIUrl":"10.1016/j.physd.2025.135101","url":null,"abstract":"<div><div>This study presents a systematic investigation of modulational instability and nonlinear wave dynamics in the reverse space-time fifth-order nonlinear Schrödinger equation. Particular focus is given to rogue wave generation and multi-pole soliton interactions. The modulational instability analysis predicts the emergence of rogue waves and rogue wave-rational soliton transitions in the focusing regime. Higher-order rogue wave solutions are constructed through generalized Darboux transformation. Notably, we introduce energy spectrum to investigate the dynamic behaviors of rogue waves. Furthermore, we derive multi-pole soliton solutions and rigorously establish their asymptotic decomposition into weakly interacting fundamental solitons. The results significantly advance the understanding of nonlinear waves in high-order nonlocal integrable systems.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"488 ","pages":"Article 135101"},"PeriodicalIF":2.9,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145928017","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 Mach number on shock-induced evolution of a cylinder with and without a cavity under transcritical conditions","authors":"Yu Jiao ,&nbsp;Steffen J. Schmidt ,&nbsp;Nikolaus A. Adams","doi":"10.1016/j.physd.2025.135102","DOIUrl":"10.1016/j.physd.2025.135102","url":null,"abstract":"<div><div>This study numerically investigates the interaction of planar shock waves with cavity-embedded n-dodecane fuel cylinders under transcritical thermodynamic conditions. Fourteen cases with Mach numbers ranging from 1.2 to 2.1 are simulated using the finite-volume compressible multi-component solver CAvitation Technical University of Munich (CATUM), incorporating an optimized WENO3 reconstruction scheme and a modified Peng–Robinson equation of state. The numerical approach is validated against reference data, and mesh convergence is confirmed through four levels of grid refinement. The analysis highlights the influence of Mach number on wave dynamics, structural deformation, vorticity deposition, circulation growth, and enstrophy evolution. Compared with full-cylinder configurations, cavity-embedded cylinders undergo earlier deformation, faster downstream displacement, and stronger vorticity generation, leading to enhanced fuel–nitrogen mixing, with the effect becoming more pronounced at higher Mach numbers. Quantitative comparisons demonstrate that the proposed modified Zhang–Zou (M-ZZ) model reliably predicts circulation deposition across all examined Mach numbers, with errors of less than 10%. To assess cavity effects, a transcritical-enstrophy model (TEM) is developed, which predicts enstrophy evolution with errors below 12%. In particular, at Mach 2.0 the enstrophy of the cavity case is about 20% higher than that of the non-cavity case, representing the most significant enhancement among all examined conditions. Cavity-induced mechanisms substantially enhance mixing efficiency, which is evidenced by an increase in enstrophy of more than 10% under stronger shocks. These findings provide insights into instability-driven mixing processes in transcritical environments.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"488 ","pages":"Article 135102"},"PeriodicalIF":2.9,"publicationDate":"2025-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145928015","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":"Modulation of fast and slow magnetosonic waves in a magnetorotating quantum plasma","authors":"Mahmood A.H. Khaled ,&nbsp;Yusra A.A. Hager ,&nbsp;Mohamed A. Shukri","doi":"10.1016/j.physd.2025.135096","DOIUrl":"10.1016/j.physd.2025.135096","url":null,"abstract":"<div><div>The amplitude modulation of fast and slow magnetosonic (MS) waves was investigated in a magnetorotating collisional electron-ion degenerate plasma. Based on the quantum magnetohydrodynamic (QMHD) model and the reductive perturbation technique, the dissipative nonlinear Schrödinger equation was developed with the inclusion of the effects of quantum statistics, quantum diffraction, magnetization force, and rotation influences. The contemplated system supported both fast and slow MS waves. The nonlinear dispersions of the MS waves and the nature of the modulation instabilities were analyzed to determine the stable and unstable regions of the modulated waves. It was found that the inclusion of rotation significantly modified the modulation instability (MI) of the MS wave packet. Alternatively, stationary envelope solitary waves could not propagate in the considered plasma as a result of the dissipative impacts. The aspects of dissipative MS rogue waves were discussed due to the regarded plasma parameters. Our results provide a better understanding of the excitation of dissipative rogue waves in laboratory experiments and astrophysical environments, such as neutron stars and white dwarfs.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"488 ","pages":"Article 135096"},"PeriodicalIF":2.9,"publicationDate":"2025-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145928019","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}