Physica D: Nonlinear Phenomena最新文献

{"title":"Through and beyond moments, entropies and Fisher information measures: new informational functionals and inequalities","authors":"Razvan Gabriel Iagar,&nbsp;David Puertas-Centeno","doi":"10.1016/j.physd.2025.134928","DOIUrl":"10.1016/j.physd.2025.134928","url":null,"abstract":"<div><div>We introduce new classes of informational functionals, called <em>upper moments</em>, respectively <em>down-Fisher measures</em>, obtained by applying classical functionals such as <span><math><mi>p</mi></math></span>-moments and the Fisher information to the recently introduced up or down transformed probability density functions. We extend some of the most important informational inequalities to our new functionals and establish optimal constants and minimizers for them. In particular, we highlight that, under certain constraints, the generalized Beta probability density maximizes (or minimizes) the upper-moments when the moment is fixed. Moreover, we apply these structured inequalities to systematically establish new and sharp upper bounds for the main classical informational products such as moment–entropy, Stam, or Cramér–Rao like products under certain regularity conditions. Other relevant properties, such as regularity under scaling changes or monotonicity with respect to the parameter, are studied. Applications to related problems to the Hausdorff moment problem are also given.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 134928"},"PeriodicalIF":2.9,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145159065","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":"Modeling late-time sensitivity to initial conditions in Boussinesq Rayleigh–Taylor turbulence","authors":"Sébastien Thévenin ,&nbsp;Benoît-Joseph Gréa","doi":"10.1016/j.physd.2025.134947","DOIUrl":"10.1016/j.physd.2025.134947","url":null,"abstract":"<div><div>This article sheds light on the influence of initial conditions in Boussinesq Rayleigh–Taylor turbulence. It builds on the related paper from Thévenin et al. (2025), which introduces a physics-informed neural network that effectively extrapolates the dynamics to very late times and unseen initial conditions, beyond the reach of direct numerical simulations. The present paper focuses on the self-similar regime and combines machine learning, variance-based sensitivity analysis and theory to provide a robust understanding of the late-time dependency on initial conditions. Particular emphasis is placed on the virtual time origin, which is shown to strongly vary with the initial Reynolds, perturbation steepness and bandwidth numbers. We develop an analytical model based on the phenomenology of Rayleigh–Taylor mixing layers to explain most of this dependency and give accurate predictions of the virtual time origin. It turns out that when the initial perturbation reaches nonlinear saturation earlier, the mixing layer also re-accelerates earlier, while the virtual time origin is larger.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 134947"},"PeriodicalIF":2.9,"publicationDate":"2025-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145159064","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":"Inverse problems related to electrical networks and the geometry of non-negative Grassmannians","authors":"A.A. Kazakov","doi":"10.1016/j.physd.2025.134948","DOIUrl":"10.1016/j.physd.2025.134948","url":null,"abstract":"<div><div>We provide a new solution to the classical black box problem (the discrete Calderón problem) in the theory of circular electrical networks. Our approach is based on the explicit embedding of electrical networks into non-negative Grassmannians and generalized chamber ansatz for it. Also, we reveal the relation of this problem with the combinatorial properties of spanning groves and the theory of totally non-negative matrices.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 134948"},"PeriodicalIF":2.9,"publicationDate":"2025-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145154747","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 assimilation and local-in-time global control of inviscid systems using partially resolved measurements","authors":"Abhishek Balakrishna ,&nbsp;Elizabeth Carlson ,&nbsp;Pranava Chaitanya Jayanti","doi":"10.1016/j.physd.2025.134929","DOIUrl":"10.1016/j.physd.2025.134929","url":null,"abstract":"<div><div>Most data assimilation algorithms have focused on dissipative systems, as the method relies on the existence of a global attractor. In this paper, we extend the framework of continuous data assimilation to inviscid models. As a first step towards this goal, we consider two inviscid systems: the passive scalar transport equation and the Euler equation. The data assimilation algorithm we employ utilizes nudging, a method based on a Newtonian relaxation scheme motivated by feedback control. We consider the two systems in an analytic space with a time-dependent analytic radius. This allows us to extract an artificial dissipative term, which is necessary for the application of data assimilation techniques. We establish exponential decay of the error between the data assimilated solution and the reference solution on a finite time interval <span><math><mrow><mo>[</mo><mn>0</mn><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mo>∗</mo></mrow></msub><mo>)</mo></mrow></math></span>, and estimate the error at the end of the algorithm (as <span><math><mrow><mi>t</mi><mo>→</mo><msub><mrow><mi>T</mi></mrow><mrow><mo>∗</mo></mrow></msub></mrow></math></span>).</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 134929"},"PeriodicalIF":2.9,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097238","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 modulational instability, classifications and dynamical properties of the localized wave solutions in the Hirota equation","authors":"Zheng Liu ,&nbsp;Hongli An ,&nbsp;Liying Hou ,&nbsp;Yao Chen","doi":"10.1016/j.physd.2025.134913","DOIUrl":"10.1016/j.physd.2025.134913","url":null,"abstract":"<div><div>In this paper, we introduce the generalized perturbation (<span><math><mrow><mi>n</mi><mo>,</mo><mi>N</mi></mrow></math></span>-<span><math><mi>n</mi></math></span>)-fold Darboux transformation (gDT) to investigate the Hirota equation, which has been viewed as a better physical model to accurately describe wave propagations in the ocean and optical fibers than the NLS equation. Firstly, we analyze the modulational instability and build the mechanism of generating different localized waves for the Hirota equation. Then, by using (<span><math><mrow><mi>n</mi><mo>,</mo><mi>N</mi></mrow></math></span>-<span><math><mi>n</mi></math></span>)-fold gDT, we obtain abundant localized wave solutions, including higher-order rogue waves (RWs), higher-order periodic waves and their interactions. Dynamical properties of these solutions are investigated numerically and theoretically. Based on the detailed numerical and theoretical analysis, we make a classification of the higher-order RWs based on their structures. In particular, for the first-order RWs, we give the analytical formulas of their length and width via the contour line method. And for the second-order RWs, we prove that the three first-order RWs after splitting are the same when the modulation parameters tend to infinity via the large-parameter asymptotic analysis. The method adopted here can be extended to construct localized waves of other nonlinear systems. The results obtained are new and they may provide a new perspective or reference in understanding the related rogue wave phenomenon in fluids, plasmas, nonlinear optics and Bose–Einstein condensation.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 134913"},"PeriodicalIF":2.9,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097243","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 sufficient frameworks for the exponential thermo-mechanical flocking in inertial spin ensembles","authors":"Seung-Yeal Ha ,&nbsp;Guanghui Jin ,&nbsp;Myeonghyeon Kim ,&nbsp;Qirui Wang","doi":"10.1016/j.physd.2025.134946","DOIUrl":"10.1016/j.physd.2025.134946","url":null,"abstract":"<div><div>We study quantitative flocking estimates for two thermo-mechanical inertial spin models. More precisely, we present a sufficient framework leading to the exponential decay of each thermo-mechanically consistent inertial spin model. For this, we derive a system of differential inequalities for relative kinetic and spin energies, when thermal and linear velocities are confined in an invariant cone, and then we explicitly obtain exponential flocking under the proposed frameworks. We also provide several numerical examples and compare them with analytical results.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 134946"},"PeriodicalIF":2.9,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097239","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":"Triangular rogue clusters associated with multiple roots of Adler–Moser polynomials in integrable systems","authors":"Bo Yang ,&nbsp;Jianke Yang","doi":"10.1016/j.physd.2025.134921","DOIUrl":"10.1016/j.physd.2025.134921","url":null,"abstract":"<div><div>Rogue patterns associated with multiple roots of Adler–Moser polynomials under general multiple large parameters of single-power form are studied in integrable systems. It is first shown that the multiplicity of any multiple root in any Adler–Moser polynomial is a triangular number (i.e., its multiplicity is equal to <span><math><mrow><mi>n</mi><mrow><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mo>/</mo><mn>2</mn></mrow></math></span> for a certain integer <span><math><mi>n</mi></math></span>). Then, it is shown that corresponding to a nonzero multiple root of the Adler–Moser polynomial, a triangular rogue cluster would appear on the spatial–temporal plane. This triangular rogue cluster comprises <span><math><mrow><mi>n</mi><mrow><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mo>/</mo><mn>2</mn></mrow></math></span> fundamental rogue waves forming a triangular shape, and space–time locations of fundamental rogue waves in this triangle are a linear transformation of the Yablonskii–Vorob’ev polynomial <span><math><mrow><msub><mrow><mi>Q</mi></mrow><mrow><mi>n</mi></mrow></msub><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow></mrow></math></span>’s root structure. In the special case where this multiple root of the Adler–Moser polynomial is zero, the associated rogue pattern is found to be an <span><math><mi>n</mi></math></span>th order rogue wave in the <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span> neighborhood of the spatial–temporal origin. These general results are demonstrated on two integrable systems: the nonlinear Schrödinger equation and the generalized derivative nonlinear Schrödinger equation. For these equations, asymptotic predictions of rogue patterns are compared with true rogue solutions and good agreement between them is illustrated. The present results generalize the earlier ones in the literature where only one of the parameters was assumed large. Extension of these results to generic multiple large parameters of dual-power form is also discussed.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 134921"},"PeriodicalIF":2.9,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145118817","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":"Breather interactions in the integrable discrete Manakov system and trigonometric Yang–Baxter maps","authors":"V. Caudrelier ,&nbsp;N.J. Ossi ,&nbsp;B. Prinari","doi":"10.1016/j.physd.2025.134917","DOIUrl":"10.1016/j.physd.2025.134917","url":null,"abstract":"<div><div>The goal of this work is to obtain a complete characterization of soliton and breather interactions in the integrable discrete Manakov (IDM) system, a vector generalization of the Ablowitz-Ladik model. The IDM system, which in the continuous limit reduces to the Manakov system (i.e., a 2-component vector nonlinear Schrödinger equation), was shown to admit a variety of discrete vector soliton solutions: fundamental solitons, fundamental breathers, and composite breathers. While the interaction of fundamental solitons was studied early on, no results are presently available for other types of soliton-breather and breather-breather interactions. Our study reveals that upon interacting with a fundamental breather, a fundamental soliton becomes a fundamental breather. Conversely, the interaction of two fundamental breathers generically yields two fundamental breathers with polarization shifts, but may also result in a fundamental soliton and a fundamental breather. Composite breathers interact trivially both with each other and with a fundamental soliton or breather. Explicit formulas for the scattering coefficients that characterize fundamental and composite breathers are given. This allows us to interpret the interactions in terms of a refactorization problem and derive the associated Yang–Baxter maps describing the effect of interactions on the polarizations. These give the first examples of parametric Yang–Baxter maps of trigonometric type.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 134917"},"PeriodicalIF":2.9,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097245","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":"Asymptotic integrability and its consequences","authors":"A.M. Kamchatnov","doi":"10.1016/j.physd.2025.134944","DOIUrl":"10.1016/j.physd.2025.134944","url":null,"abstract":"<div><div>We give a brief review of the concept of asymptotic integrability, which means that the Hamilton equations for the propagation of short-wavelength packets along a smooth, large-scale background wave have an integral independent of the initial conditions. The existence of such an integral leads to a number of important consequences, which include, besides the direct application to the packets propagation problems, Hamiltonian theory of narrow solitons motion and generalized Bohr–Sommerfeld rule for parameters of solitons produced from an intensive initial pulse. We show that in the case of systems with two wave variables and exact fulfillment of the asymptotic integrability condition, the ‘quantization’ of mechanical systems, associated with the additional integrals, yields the Lax pairs for a number of typical completely integrable equations, and this sheds new light on the origin of the complete integrability in nonlinear wave physics.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 134944"},"PeriodicalIF":2.9,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097246","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":"Braided Gelfand–Zetlin algebras and their semiclassical counterparts","authors":"Dimitry Gurevich ,&nbsp;Pavel Saponov","doi":"10.1016/j.physd.2025.134940","DOIUrl":"10.1016/j.physd.2025.134940","url":null,"abstract":"<div><div>We construct analogs of the Gelfand–Zetlin algebras in the Reflection Equation algebras, corresponding to Hecke symmetries, mainly to those coming from the Quantum Groups <span><math><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi>q</mi></mrow></msub><mrow><mo>(</mo><mi>s</mi><mi>l</mi><mrow><mo>(</mo><mi>N</mi><mo>)</mo></mrow><mo>)</mo></mrow></mrow></math></span>. Corresponding semiclassical (i.e. Poisson) counterparts of the Gelfand–Zetlin algebras are described.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 134940"},"PeriodicalIF":2.9,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145109621","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}