Physica D: Nonlinear Phenomena最新文献

{"title":"Three-to-one internal resonances between acoustic and optical waves in metamaterials with nonlinear resonators","authors":"Laura Di Gregorio,&nbsp;Walter Lacarbonara","doi":"10.1016/j.physd.2025.134748","DOIUrl":"10.1016/j.physd.2025.134748","url":null,"abstract":"<div><div>We investigate the modal interactions between two generalized oscillators representing the acoustic and optical waves obtained as solutions of the wave propagation equations across a metamaterial conceived as cellular hosting 2D structure augmented by intracellular resonators. Without damping, the system is Hamiltonian, with the origin as an elliptic equilibrium characterized by two distinct linear frequencies. To understand the underlying dynamics, it is crucial to derive explicit analytical formulae for the nonlinear frequencies as functions of the physical parameters. In the small amplitude regime (perturbative case), we provide the first-order nonlinear correction to the linear frequencies. While this analytic expression was already derived for non-resonant cases, the interest is here placed on wave interactions in the context of resonant or nearly resonant scenarios. In particular, we focus on 3:1 internal resonance, the only resonance involved in the first-order correction. We then address the challenging strongly resonant case in which the detuning is small with respect to the perturbative parameter. Unlike standard approaches, here we capture the full complexity of resonant dynamics, revealing a richer, more intricate topological features. Utilizing the Hamiltonian structure, we employ Perturbation Theory to transform the system into Birkhoff Normal Form up to order four. This involves converting the system into action–angle variables, where the truncated Hamiltonian at order four depends on the actions and, due to the resonance, on one “slow” angle. By constructing suitable nonlinear and not close-to-the-identity coordinate transformations, we identify new sets of symplectic action–angle variables. In these variables, the resulting system is integrable up to higher-order terms, meaning it does not depend on the angles, and the frequencies are obtained from the derivatives of the energy with respect to the actions. This construction is highly dependent on the physical parameters, necessitating a detailed case analysis of the phase portrait, which reveals up to six topologically distinct behaviors. In each instance, we describe the nonlinear normal modes (elliptic/hyperbolic periodic orbits, invariant tori) and their stable and unstable manifolds of the truncated Hamiltonian. For the computations, we examine resonant wave interactions in metamaterial honeycombs with periodically distributed Duffing-type resonators, specifically addressing the nonlinear effects on the bandgap. More precisely, in view of the metamaterial design, our analysis allows one to identify the values of the modal mass and stiffness of the resonators, that maximize the beneficial effect of nonlinearity in enlarging the bandgap width.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134748"},"PeriodicalIF":2.7,"publicationDate":"2025-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144194493","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 simple three-component mixing problem for the evaluation of a new reaction rate model","authors":"Brandon E. Morgan,&nbsp;Kevin Ferguson","doi":"10.1016/j.physd.2025.134718","DOIUrl":"10.1016/j.physd.2025.134718","url":null,"abstract":"<div><div>A simple computational mixing problem is presented which can be utilized to assess the behavior of Reynolds-averaged reaction rate models in a problem with temporally varying mixedness. In this problem, three mixing components are homogeneously distributed but initially separated in a triply periodic domain. These components are initialized within a Taylor–Green-like velocity field, which creates a mixing history evolving from the so-called “no-mix limit” to a well-mixed state. Large-eddy simulation results from this problem in configurations involving both premixed and nonpremixed reactants are then compared with zero-dimensional Reynolds-averaged Navier–Stokes results utilizing a new model for multicomponent reacting mixtures. The new model is shown to appropriately respect the no-mix limit and outperforms an earlier model (Morgan, 2022), particularly at early times when components are near the no-mix limit.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134718"},"PeriodicalIF":2.7,"publicationDate":"2025-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144205398","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":"Analytical properties of Stoyanov step bunches: Solutions, scaling, stationary profiles","authors":"Vassil Ivanov","doi":"10.1016/j.physd.2025.134755","DOIUrl":"10.1016/j.physd.2025.134755","url":null,"abstract":"<div><div>Within the framework of the Stoyanov–Tonchev equation, which describes the surface height evolution during the vicinal sublimation process affected by the electromigration of the adatoms, we explore further the stationary profiles of step bunches towards obtaining a closed-form solution. For this particular case, we derive an explicit analytical result for the slope-height relation for the bunches, and many of the well-known scaling results for the height and width of the bunch. A novel analytical approximation for the bunch profile <span><math><mrow><mi>h</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span> is derived, leading to a scaling relation for the minimal step-step distance in the bunch formed as a product of two parts - a special combination of the initial parameters, with the dimension of length, and a complementary one that contains only the number of steps in the bunch.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134755"},"PeriodicalIF":2.7,"publicationDate":"2025-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144213305","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 novel underwater weak signal detection method based on High-order double-coupled duffing oscillator, Empirical wavelet transform and Hilbert transform","authors":"Yupeng Shen ,&nbsp;Zhe Chen ,&nbsp;Yaan Li ,&nbsp;Weijia Li","doi":"10.1016/j.physd.2025.134775","DOIUrl":"10.1016/j.physd.2025.134775","url":null,"abstract":"<div><div>The increasing complexity of marine noise environments and advancements in stealth technology have significantly weakened the continuous spectrum of underwater signals, rendering traditional random signal analysis methods inadequate for weak signal detection amidst complex noise backgrounds. To address the challenge of detecting underwater weak signals at ultra-low Signal-to-Noise Ratios (SNR), we propose a novel detection method that integrates high-order double-coupled Duffing oscillator, Empirical Wavelet Transform (EWT), and Hilbert Transform. This approach begins with the introduction of a novel high-order double-coupled Duffing oscillator, whose dynamic behavior is thoroughly analyzed using nonlinear techniques, including Lyapunov exponents, bifurcation analysis, and entropy measures. The analysis proves that the improved Duffing oscillator has excellent robustness to different noise. Then, combined with the constructed geometric frequency array and the scale transformation, a new weak signal detection array that can detect any frequency is constructed. The system discerns the presence of underwater signals by monitoring changes in the attractor trajectory, specifically transitions from chaotic behavior to large-period or intermittent chaos. Finally, a novel frequency extraction method that leverages EWT and Hilbert Transform is proposed, which can achieve noise reduction and kurtosis optimization for intermittent chaotic signals, thereby extracting the actual frequency of underwater weak signals. Experimental results confirm that the proposed detection array effectively identifies underwater weak signals submerged in complex noise environments, achieving a detection SNR of -38.42 dB and an extracted signal frequency error of &lt;1 %. The simulation results meet the stringent accuracy requirements for underwater sonar applications.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134775"},"PeriodicalIF":2.7,"publicationDate":"2025-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144221999","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 stability and instability of plasma boundary layers","authors":"Masahiro Suzuki ,&nbsp;Masahiro Takayama ,&nbsp;Katherine Zhiyuan Zhang","doi":"10.1016/j.physd.2025.134743","DOIUrl":"10.1016/j.physd.2025.134743","url":null,"abstract":"<div><div>We investigate the formation of a plasma boundary layer (sheath) by considering the Vlasov–Poisson system on a half space with the completely absorbing boundary condition. In Suzuki and Takayama (2023), the solvability of the stationary problem is studied. In this paper, we study the nonlinear stability and instability of these stationary solutions of the Vlasov–Poisson system.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134743"},"PeriodicalIF":2.7,"publicationDate":"2025-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144205651","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":"Internal solitary and cnoidal waves of moderate amplitude in a two-layer fluid: the extended KdV equation approximation","authors":"Nerijus Sidorovas ,&nbsp;Dmitri Tseluiko ,&nbsp;Wooyoung Choi ,&nbsp;Karima Khusnutdinova","doi":"10.1016/j.physd.2025.134723","DOIUrl":"10.1016/j.physd.2025.134723","url":null,"abstract":"<div><div>We consider travelling internal waves in a two-layer fluid with linear shear currents from the viewpoint of the extended Korteweg–de Vries (eKdV) equation derived from a strongly-nonlinear long-wave model. Using an asymptotic Kodama-Fokas-Liu near-identity transformation, we map the eKdV equation to the Gardner equation. This improved Gardner equation has a different cubic nonlinearity coefficient and an additional transport term compared to the frequently used truncated Gardner equation. We then construct approximate solitary and cnoidal wave solutions of the eKdV equation using this mapping and test validity and performance of these approximations, as well as performance of the truncated and improved Gardner and eKdV equations, by comparison with direct numerical simulations of the strongly-nonlinear two-layer long-wave parent system in the absence of currents.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134723"},"PeriodicalIF":2.7,"publicationDate":"2025-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144205397","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 class of exact solutions of the Ishimori equation","authors":"Rustem N. Garifullin,&nbsp;Ismagil T. Habibullin","doi":"10.1016/j.physd.2025.134746","DOIUrl":"10.1016/j.physd.2025.134746","url":null,"abstract":"<div><div>In this paper, a class of particular solutions of the Ishimori equation is found. This equation is known as the spatially two-dimensional version of the Heisenberg equation, which has important applications in the theory of ferromagnets. It is shown that the two-dimensional Toda-type lattice found earlier by Ferapontov, Shabat and Yamilov is a dressing chain for this equation. Using the integrable reductions of the dressing chain, the authors found an essentially new class of solutions to the Ishimori equation.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"480 ","pages":"Article 134746"},"PeriodicalIF":2.7,"publicationDate":"2025-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144185223","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":"Steady compressible 3D Euler flows in toroidal volumes without continuous Euclidean isometries","authors":"Naoki Sato ,&nbsp;Michio Yamada","doi":"10.1016/j.physd.2025.134741","DOIUrl":"10.1016/j.physd.2025.134741","url":null,"abstract":"<div><div>We demonstrate the existence of smooth three-dimensional vector fields where the cross product between the vector field and its curl is balanced by the gradient of a smooth function, with toroidal level sets that are not invariant under continuous Euclidean isometries. This finding indicates the existence of steady compressible Euler flows, either influenced by an external potential energy or maintained by a density source in the continuity equation, that are foliated by asymmetric nested toroidal surfaces. Our analysis suggests that the primary obstacle in resolving Grad’s conjecture regarding the existence of nontrivial magnetohydrodynamic equilibria arises from the incompressibility constraint imposed on the magnetic field.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"480 ","pages":"Article 134741"},"PeriodicalIF":2.7,"publicationDate":"2025-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144169732","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":"Direct linearisation of the non-commutative Kadomtsev–Petviashvili equations","authors":"Gordon Blower ,&nbsp;Simon J.A. Malham","doi":"10.1016/j.physd.2025.134745","DOIUrl":"10.1016/j.physd.2025.134745","url":null,"abstract":"<div><div>We prove that the non-commutative Kadomtsev–Petviashvili (KP) equation and a ‘lifted’ modified Kadomtsev–Petviashvili (mKP) equation are directly linearisable, and thus integrable in this sense. There are several versions of the non-commutative mKP equations, including the two-dimensional generalisations of the non-commutative modified Korteweg–de Vries (mKdV) equation and its alternative form (amKdV). Herein we derive the ‘lifted’ mKP equation, whose solutions are the natural two-dimensional extension of those for the non-commutative mKdV equation derived in Blower and Malham (2023). We also present the log-potential form of the mKP equation, from which all of these non-commutative mKP equations can be derived. To achieve the integrability results, we construct the pre-Pöppe algebra that underlies the KP and mKP equations. This is a non-commutative polynomial algebra over the real line generated by the solution (and its partial derivatives) to the linearised form of the KP and mKP equations. The algebra is endowed with a pre-Pöppe product, based on the product rule for semi-additive operators pioneered by Pöppe for the commutative KP equation. Integrability corresponds to establishing a particular polynomial expansion in the respective pre-Pöppe algebra. We also present numerical simulations of soliton-like interactions for the non-commutative KP equation.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134745"},"PeriodicalIF":2.7,"publicationDate":"2025-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144221998","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":"Pulse solutions in Gierer–Meinhardt equation with slowly degenerate nonlinearity","authors":"Yuanxian Chen ,&nbsp;Jianhe Shen","doi":"10.1016/j.physd.2025.134738","DOIUrl":"10.1016/j.physd.2025.134738","url":null,"abstract":"<div><div>Based on geometric singular perturbation theory (GSPT) and nonlocal eigenvalue problem (NLEP) method, this article studies the existence and stability of algebraically delaying pulses in Gierer–Meinhardt equation with slowly degenerate nonlinearity. By utilizing the fact that the critical manifold is both normally hyperbolic and invariant, we rigorously establish the existence of algebraically decaying pulses by combining GSPT with the Melnikov method. It is proven that the model has a unique algebraically decaying pulse. On the other hand, the slowly degenerate nonlinearity results in that the linearized matrix associated with the eigenvalue problem no longer approaches the constant matrix exponentially. Hence, we must solve the resulting linear “time-varying” problem. By classifying the power of the slowly degenerate nonlinearity, we introduce different special functions including the Whittaker function and the Bessel function to solve this linear problem explicitly. Thus the spectral (in)stability criteria on the algebraically delaying pulse can be set up by matching the slow and fast segments of the eigenfunctions. An example is also provided to illustrate the theoretical framework.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134738"},"PeriodicalIF":2.7,"publicationDate":"2025-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144205650","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}