Physica D: Nonlinear Phenomena最新文献

{"title":"Thermocapillary ultrathin self-rewetting film flows down a rotating fibre","authors":"Souradip Chattopadhyay","doi":"10.1016/j.physd.2025.134843","DOIUrl":"10.1016/j.physd.2025.134843","url":null,"abstract":"<div><div>This study investigates the influence of thermocapillarity on the dynamics and nonlinear stability of an ultrathin self-rewetting film flowing down a uniformly heated rotating vertical fibre. To capture the combined effects of intermolecular forces (van der Waals attraction) and centrifugal forces (due to rotation), a thin-film evolution equation is derived, assuming the film thickness is much smaller than the fibre radius. Linear stability analysis shows that the van der Waals attraction and rotation always enhance instability, whether acting alone or together. The impact of thermocapillarity in the presence of both van der Waals attraction and rotation on absolute/convective instability is also discussed. When <span><math><mrow><msup><mrow><mi>T</mi></mrow><mrow><mi>i</mi></mrow></msup><mo>&lt;</mo><msub><mrow><mi>T</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></math></span>, where <span><math><msup><mrow><mi>T</mi></mrow><mrow><mi>i</mi></mrow></msup></math></span> is the interfacial temperature and <span><math><msub><mrow><mi>T</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> is the temperature at which surface tension is minimum, absolute instability occurs at a lower Marangoni number compared to the case where van der Waals attraction and rotation are absent. When <span><math><mrow><msup><mrow><mi>T</mi></mrow><mrow><mi>i</mi></mrow></msup><mo>&gt;</mo><msub><mrow><mi>T</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></math></span>, the convective instability region expands with a higher Marangoni number, even when van der Waals attraction and rotation are present. A weakly nonlinear analysis using the method of multiple scales is conducted to study the bifurcation behavior of the nonlinear evolution equation. The results indicate the existence of both subcritical and supercritical regimes and demonstrate how thermocapillarity, combined with rotation and van der Waals forces, influences the shift of the bifurcation point. Finally, numerical simulations of the nonlinear evolution equation are performed for various flow parameters. These results explain how rotation, thermal effects, and intermolecular forces influence the flow dynamics.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134843"},"PeriodicalIF":2.9,"publicationDate":"2025-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144724586","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":"Integrable variants of the Leznov lattice and the differential-difference KP equations","authors":"Ya-Jie Liu ,&nbsp;Hui Alan Wang ,&nbsp;Xing-Biao Hu ,&nbsp;Ying-Nan Zhang","doi":"10.1016/j.physd.2025.134831","DOIUrl":"10.1016/j.physd.2025.134831","url":null,"abstract":"<div><div>By introducing trigonometric-type bilinear operators, we propose two novel discrete integrable equations that can be viewed as variants of the Leznov lattice and the differential-difference Kadomtsev–Petviashvili (D<span><math><mi>Δ</mi></math></span>KP) equations. It turns out that both equations admit various solutions, including general Grammian determinant, soliton, lump, rogue wave, and breather solutions, which are expressed by explicit and closed forms. Moreover, <span><math><mi>g</mi></math></span>-periodic wave solutions are also constructed in terms of Riemann theta function. Numerical three-periodic wave solutions are successfully computed by using a deep neural network. Finally, we construct a continuum limit, through which we reveal clear links between the variant D<span><math><mi>Δ</mi></math></span>KP equation and the Kadomtsev–Petviashvili-I (KPI) equation from both the equation and solution perspectives.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134831"},"PeriodicalIF":2.9,"publicationDate":"2025-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144830992","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":"Numerical analysis on the effect of obstacles in the mixing dynamics of a supersonic natural gas jet","authors":"Ignacio Zamudio-Fernández,&nbsp;Martín Salinas-Vázquez,&nbsp;William Vicente","doi":"10.1016/j.physd.2025.134840","DOIUrl":"10.1016/j.physd.2025.134840","url":null,"abstract":"<div><div>The mixing dynamics of a supersonic natural gas jet in different tubes was investigated numerically using Large Eddy Simulation (LES). The three-dimensional geometries of eight tubes were evaluated to compare pressure, mass fraction, and velocity field evolution; a straight cylindrical tube serves as the reference case. Two cases feature tubes narrowing towards the outlet (one with 2.2 degrees of inclination and another with 3.7 degrees of inclination), and five other cases with 2.2 degrees of inclination and one, two, three, four, or six obstacles added—which decrease the tube diameter. The code employed in this study was validated against three jet cases, showing good agreement with experimental and numerical data. Turbulent regions coincided with regions of maximum natural gas mass fraction. As the number of obstacles increases in each case, mixing enhancement, turbulent regions and pressure gains were higher. The cases with the most obstacles were found to be the ones that had the best mixing enhancement as well as the greatest pressure gains along the length of the tube. The best performing case had an increase in natural gas mass fraction of 13% and in pressure gains of 5% with respect to the reference case, as well as a faster advancement of natural gas. Obstacles too close to the nozzle reduced natural gas advancement and velocity.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134840"},"PeriodicalIF":2.9,"publicationDate":"2025-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144724588","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":"Quasi-periodic solutions for the nonlinear quantum harmonic oscillator","authors":"Jianjun Liu ,&nbsp;Caihong Qi ,&nbsp;Guanghua Shi","doi":"10.1016/j.physd.2025.134846","DOIUrl":"10.1016/j.physd.2025.134846","url":null,"abstract":"<div><div>This paper is concerned with the nonlinear quantum harmonic oscillator equation <span><span><span><math><mrow><mi>i</mi><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mo>−</mo><msub><mrow><mi>u</mi></mrow><mrow><mi>x</mi><mi>x</mi></mrow></msub><mo>+</mo><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>u</mi><mo>+</mo><msup><mrow><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup><mi>u</mi><mo>,</mo><mspace></mspace><mspace></mspace><mspace></mspace><mi>x</mi><mo>∈</mo><mi>R</mi><mo>.</mo></mrow></math></span></span></span>It is proved that there are Cantor families of 2-dimensional elliptic invariant tori, and thus quasi-periodic solutions for the above equation. The proof is based on infinite dimensional KAM theory and partial Birkhoff normal form. Compared with previous KAM results for quantum harmonic oscillator, the novelty lies in the above equation not containing external parameters. This gives rise to the difficulty associated with complete resonance of frequencies.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134846"},"PeriodicalIF":2.9,"publicationDate":"2025-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144721283","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":"Generation and interaction of quartic soliton-like pulses in an optical cavity","authors":"Sabrina Hetzel ,&nbsp;Alejandro Aceves","doi":"10.1016/j.physd.2025.134829","DOIUrl":"10.1016/j.physd.2025.134829","url":null,"abstract":"<div><div>Quartic solitons have emerged as viable alternative to classical solitons for different optical applications. This work presents theoretical and numerical studies on the generation and interactions of single and multiple pulses when the dispersion is of fourth order under different realizations.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134829"},"PeriodicalIF":2.7,"publicationDate":"2025-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144712967","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 capillary rise with a slip boundary condition: Well-posedness and long-time dynamics of solutions to Washburn’s equation","authors":"Isidora Rapajić ,&nbsp;Srboljub Simić ,&nbsp;Endre Süli","doi":"10.1016/j.physd.2025.134842","DOIUrl":"10.1016/j.physd.2025.134842","url":null,"abstract":"<div><div>The aim of this paper is to extend Washburn’s capillary rise equation by incorporating a slip condition at the pipe wall. The governing equation is derived using fundamental principles from continuum mechanics. A new scaling is introduced, allowing for a systematic analysis of different flow regimes. We prove the global-in-time existence and uniqueness of a bounded positive solution to Washburn’s equation that includes the slip parameter, as well as the continuous dependence of the solution in the maximum norm on the initial data. Thus, the initial-value problem for Washburn’s equation is shown to be well-posed in the sense of Hadamard. Additionally, we show that the unique equilibrium solution may be reached either monotonically or in an oscillatory fashion, similarly to the no-slip case. Finally, we determine the basin of attraction for the system, ensuring that the equilibrium state will be reached from the initial data we impose. These results hold for any positive value of the nondimensional slip parameter in the model, and for all values of the ratio <span><math><mrow><msub><mrow><mi>h</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>/</mo><msub><mrow><mi>h</mi></mrow><mrow><mi>e</mi></mrow></msub></mrow></math></span> in the range <span><math><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>3</mn><mo>/</mo><mn>2</mn><mo>]</mo></mrow></math></span>, where <span><math><msub><mrow><mi>h</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> is the initial height of the fluid column and <span><math><msub><mrow><mi>h</mi></mrow><mrow><mi>e</mi></mrow></msub></math></span> is its equilibrium height.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134842"},"PeriodicalIF":2.9,"publicationDate":"2025-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144724587","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":"Numerical evaluations of quasi-periodic wave solutions to two supersymmetric integrable equations","authors":"Zhaohua Li ,&nbsp;Zhonglong Zhao ,&nbsp;Shou-Fu Tian ,&nbsp;Yindi Liu","doi":"10.1016/j.physd.2025.134837","DOIUrl":"10.1016/j.physd.2025.134837","url":null,"abstract":"<div><div>A new algorithm named global Levenberg–Marquardt (LM) algorithm is proposed to explicitly construct quasi-periodic wave solutions of the supersymmetric integrable systems, which combines the super Riemann theta functions and Hirota’s bilinear method. In particular, the numerical quasi-periodic wave solutions for the supersymmetric KdV–Sawada–Kotera–Ramani equation and supersymmetric Ito’s equation are investigated. The quasi-periodic wave solvability problem is successfully transformed into a system of over-determined equations, which can be formulated into a least square problem and then solved by using the global LM algorithm. The quasi-periodic wave solutions can be classified into two categories including quasi-periodic parallel waves and quasi-periodic cross waves. A distinct analysis of the factors that influence the emergence of “influencing band” and the bandwidth of “influencing band” is presented. Furthermore, by using an analytical method related to the characteristic lines for the quasi-periodic waves, the dynamic characteristics including the periods, wave propagation direction, peak points, trough points, velocities and the distance between two peaks can be intuitively displayed. In addition, based on the small amplitude limit method, the asymptotic properties of <span><math><mi>N</mi></math></span>-periodic waves to the supersymmetric integrable systems are presented.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134837"},"PeriodicalIF":2.7,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144713639","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":"Topological data analysis of three dimensional orbits in a convective flow","authors":"Ahtziri González ,&nbsp;Brayan Hernández ,&nbsp;Karla P. Acosta-Zamora ,&nbsp;Eduardo Ramos ,&nbsp;José Núñez","doi":"10.1016/j.physd.2025.134841","DOIUrl":"10.1016/j.physd.2025.134841","url":null,"abstract":"<div><div>We study the topological properties of the Lagrangian orbits of natural convection in a cube with Rayleigh numbers corresponding to steady-state motion. The Lagrangian orbits are considered clusters of points distributed in a three-dimensional space. This leads to the natural application of topological data analysis (TDA) tools that include alpha complexes, 0-, 1- and 2-persistent homologies, persistence diagrams, and the bottleneck metric. For low Rayleigh numbers, the analysis is applied to orbits that correspond to a region in a Poincaré map around an elliptic point. This leads to the conclusion that the points comprising individual Lagrangian orbits are embedded on the surfaces of nested tori. For larger Rayleigh numbers, the Poincaré map includes two elliptic points separated by a chaotic region. The points composing the orbits in the three dimensional space, form two nested tori structures separated by complex and difficult to classify orbits. The bottleneck metric applied to the 0-, 1- and 2-persistence diagrams, captures a smooth evolution of the structures’ geometrical properties, suggesting an order of the orbits present in the chaotic region. Interestingly, in the region between the two nested tori structures, an orbit with topological properties similar to a trivalent 2-stratifold was found.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134841"},"PeriodicalIF":2.7,"publicationDate":"2025-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144703393","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":"Finiteness of mirror-symmetric relative equilibria of point vortices","authors":"Kevin A. O’Neil","doi":"10.1016/j.physd.2025.134823","DOIUrl":"10.1016/j.physd.2025.134823","url":null,"abstract":"<div><div>Some relative equilibrium configurations of <span><math><mi>n</mi></math></span> point vortices in the plane have a mirror symmetry. In this paper it is proved that for arbitrary <span><math><mi>n</mi></math></span> and generic choice of vortex strengths, the mirror-symmetric configurations with no more than six vortices off the line of symmetry are finite in number. The same analysis is extended to include eight off-axis vortices when restricting to <span><math><mrow><mi>n</mi><mo>=</mo><mn>8</mn></mrow></math></span>.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134823"},"PeriodicalIF":2.7,"publicationDate":"2025-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144702843","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":"Exponential-asymptotics treatment of steady radiating waves from sources of finite strength","authors":"Takeshi Kataoka ,&nbsp;T.R. Akylas","doi":"10.1016/j.physd.2025.134832","DOIUrl":"10.1016/j.physd.2025.134832","url":null,"abstract":"<div><div>We re-visit the steady forced Korteweg–deVries (fKdV) equation with a smooth locally confined forcing term and the radiation condition of no waves far upstream. When dispersion is small (<span><math><mrow><mi>μ</mi><mo>≪</mo><mn>1</mn></mrow></math></span>), nonlinearity cannot be ignored in computing the radiating wave downstream even though the wave amplitude is exponentially small relative to <span><math><mi>μ</mi></math></span>. Earlier studies computed this wave in the limit <span><math><mrow><mi>μ</mi><mo>→</mo><mn>0</mn></mrow></math></span> via exponential asymptotics, on the assumption that nonlinearity, which is controlled by the strength of the forcing term, is weak and balances with dispersion. Here, we develop a separate exponential asymptotics theory for radiating waves due to forcing of <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span> strength. A fundamental difference from previous work is that the exponent of the exponentially small factor of the wave amplitude is controlled by the forcing amplitude <span><math><mi>A</mi></math></span>, which is bound from above by a certain critical value <span><math><mrow><msub><mrow><mi>A</mi></mrow><mrow><mi>crit</mi></mrow></msub><mo>=</mo><mi>O</mi><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span>. Furthermore, this exponent tends to zero as <span><math><mi>A</mi></math></span> approaches <span><math><msub><mrow><mi>A</mi></mrow><mrow><mi>crit</mi></mrow></msub></math></span>. Thus, the present theory bridges the gap between the exponentially small waves computed earlier for <span><math><mrow><mi>A</mi><mo>≪</mo><mn>1</mn></mrow></math></span> and the steep (cnoidal) waves that arise when <span><math><mi>A</mi></math></span> is near <span><math><msub><mrow><mi>A</mi></mrow><mrow><mi>crit</mi></mrow></msub></math></span>. The asymptotic results are supported by direct numerical solutions of the fKdV equation. Furthermore, the numerical results confirm that <span><math><msub><mrow><mi>A</mi></mrow><mrow><mi>crit</mi></mrow></msub></math></span> is a limiting forcing amplitude, beyond which steady solutions diverge downstream.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134832"},"PeriodicalIF":2.7,"publicationDate":"2025-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144711187","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}