Physica D: Nonlinear Phenomena最新文献

{"title":"Critical noise for advanced dynamic B-tipping in nearly non-smooth Stommel-type models","authors":"Chris Budd ,&nbsp;Rachel Kuske","doi":"10.1016/j.physd.2025.135055","DOIUrl":"10.1016/j.physd.2025.135055","url":null,"abstract":"<div><div>We study critical relationships between the smoothness parameter for the underlying fold bifurcation and the noise level in the context of B-tipping near smooth and non-smooth dynamic fold bifurcations. The motivation is the Stommel 2-box model, a piecewise-smooth continuous dynamical system modeling thermohaline circulation in the North Atlantic, and related climate models. These contain non-smooth fold bifurcations which arise when a saddle-point and a stable focus meet at a border collision bifurcation. An asymptotic analysis of the corresponding Fokker-Planck Equation (FPE) for the stochastic system provides insight into critical noise levels, depending on the relative rate of parameter variation and a measure of smoothness of the underlying bifurcation. Critical scales are obtained from different reductions of the FPE, identifying cases where noise may advance tipping relative to deterministic behavior. Applying this approach for B-tipping near both smooth and non-smooth folds shows that the non-smooth case has greater sensitivity to smaller noise levels, with a smaller critical scale for noise-advanced tipping in the non-smooth case. Since these results do not depend on obtaining a solution of the FPE, the approach can be adapted to multi-degree-of-freedom models and in other applications.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"488 ","pages":"Article 135055"},"PeriodicalIF":2.9,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145928012","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":"2026-04-01","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":"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":"2026-04-01","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":"Fundamental hydrodynamic breathers on standing waves","authors":"Yuchen He ,&nbsp;Alexey Slunyaev ,&nbsp;Nobuhito Mori ,&nbsp;Ioannis Kourakis ,&nbsp;Amin Chabchoub","doi":"10.1016/j.physd.2025.135098","DOIUrl":"10.1016/j.physd.2025.135098","url":null,"abstract":"<div><div>Extreme wave localizations in nonlinear dispersive media, arising from modulation instability in weakly nonlinear wave interactions, can be effectively modeled by breather solutions. These breathers are exact solutions of the nonlinear Schrödinger equation and provide accurate models for understanding and controlling unidirectional rogue wave dynamics in numerical simulations or laboratory settings. A recent study by <strong>Y. He</strong> et al.<strong>, Phys. Rev. Lett. 129, 144,502 (2022)</strong> offered the first proof of concept that the distinctive focusing features of Peregrine-type breathers can persist on standing water waves, consisting of two counter-propagating wave trains with identical carrier amplitudes and frequencies. In the present work, we report comprehensive experimental observations of nonlinear wave focusing dynamics on standing waves using all three fundamental breather types: the Kuznetsov-Ma, Peregrine, and Akhmediev breathers. Additionally, we extend our investigation to scenarios in which the opposing wave field has differing amplitudes or frequencies, in order to further assess the robustness of breather propagation under this particular cross-wave condition. The experimental results show good agreement with the hydrodynamic coupled nonlinear Schrödinger equation (CNLSE) for the relevant cases and confirm that both coherence and amplitude amplification of the breathers are preserved in the presence of opposing Stokes waves. These findings further support the idea that modulation instability can prevail during the interaction of distinct wave systems, even beyond the narrowband and unidirectional assumptions of the classical theory.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"488 ","pages":"Article 135098"},"PeriodicalIF":2.9,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038329","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":"2026-04-01","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":"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":"2026-04-01","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":"Bose-Einstein condensates with density-dependent gauge potential and two PT-symmetric potentials: Solitons, rogue waves and nonlinear dynamics","authors":"Yufeng Liu ,&nbsp;Jin Song ,&nbsp;Zhenya Yan","doi":"10.1016/j.physd.2026.135117","DOIUrl":"10.1016/j.physd.2026.135117","url":null,"abstract":"<div><div>In this paper, we investigate the dynamical behaviors of soliton solutions and rogue waves in Bose-Einstein condensates, modelled by the focusing and defocusing Gross-Pitaevskii equations. Our work uniquely integrates the effects of a density-dependent gauge potential with two novel types of parity-time (<span><math><mi>PT</mi></math></span>) symmetric potentials: the generalized <span><math><mi>PT</mi></math></span>-symmetric harmonic-Gaussian potential and the generalized <span><math><mi>PT</mi></math></span>-symmetric Scarf-II potential. This specific combination provides a rich platform for exploring the phenomenon of matter waves. Firstly, we analyze the linear spectral problem to determine the entirely real spectral region of the non-Hermitian Hamiltonian and examine the occurrence of the phase-breaking phenomena. Then, we discuss the exact solutions for both types of <span><math><mi>PT</mi></math></span>-symmetric external potentials, as well as the numerical solutions for the ground state and dipole modes, while analyzing their stability using the corresponding Bogoliubov-de Gennes equations. Moreover, we investigate the effect of the current nonlinearity on the stability of exact solitons. In particular, the interactions between two solitons are studied, exhibiting nearly elastic and inelastic interactions. Furthermore, the stable adiabatic excitations of solitons are investigated. Finally, due to the influence of current nonlinearity on its structure, the high-order rogue wave generated by several Gaussian perturbations on the continuous wave undergoes a transformation into chiral solitons with lower amplitude. Our research provides in-depth insights into the dynamic behavior of solitons and rogue waves in novel systems with density-dependent gauge potential and <span><math><mi>PT</mi></math></span>-symmetric external potential, offering important guidance for future theoretical research and experimental exploration of complex matter wave phenomena.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"488 ","pages":"Article 135117"},"PeriodicalIF":2.9,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038327","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":"A Hamiltonian approach for point vortices on non-orientable surfaces","authors":"N. Balabanova ,&nbsp;J.A. Montaldi","doi":"10.1016/j.physd.2025.135084","DOIUrl":"10.1016/j.physd.2025.135084","url":null,"abstract":"<div><div>We investigate the motion of point vortices on the Möbius band and Klein bottle. Since these are non-orientable surfaces, the standard Hamiltonian approach does not apply. We therefore begin by establishing a modified Hamiltonian approach which works for arbitrary non-orientable surfaces, through describing the phase space, the Hamiltonian and the local equations of motion. We use a combination of twisted functions and oriented double covers to adapt some of the known notions of vortex dynamics to non-orientable surfaces. For both of the surfaces of interest, we write Hamiltonian-type equations of vortex motion explicitly and follow that by the description of relative equilibria and an investigation of the motion of one and two vortices.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"488 ","pages":"Article 135084"},"PeriodicalIF":2.9,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145870484","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":"2026-04-01","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":"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":"2026-04-01","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}