Physica D: Nonlinear Phenomena最新文献

{"title":"Long-time asymptotics for the massive Thirring model on the half-line","authors":"Xumeng Zhou,&nbsp;Xianguo Geng,&nbsp;Mingming Chen","doi":"10.1016/j.physd.2025.134877","DOIUrl":"10.1016/j.physd.2025.134877","url":null,"abstract":"<div><div>The asymptotic formula for the solution of the massive Thirring model on the half-line <span><math><mrow><mi>x</mi><mo>≥</mo><mn>0</mn></mrow></math></span> is derived under the assumption that the initial and boundary values lie in Schwartz space. It is shown that the solution of the massive Thirring model can represented by the solution of the derived matrix Riemann–Hilbert problem. The relevant jump matrices are explicitly given in the form of the matrix-valued spectral functions that depend on the initial data and boundary values. By applying the nonlinear steepest descent analysis of two related Riemann–Hilbert problems, one for the spectral parameter at the origin and the other for the spectral parameter at infinity, the explicit long-time asymptotic formula and uniform error estimates for the solution of the massive Thirring model are given on the half-line.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"482 ","pages":"Article 134877"},"PeriodicalIF":2.9,"publicationDate":"2025-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144918935","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":"Orbital stability and strong instability of solitary waves for the Kadomtsev–Petviashvili equation with combined power nonlinearities","authors":"Leijin Cao ,&nbsp;Binhua Feng ,&nbsp;Zhiqian He ,&nbsp;Yichun Mo","doi":"10.1016/j.physd.2025.134875","DOIUrl":"10.1016/j.physd.2025.134875","url":null,"abstract":"<div><div>In this paper, we study the orbital stability and strong instability of solitary waves for the two-dimensional Kadomtsev–Petviashvili equation with combined power nonlinearities <span><span><span><math><mrow><msub><mrow><mrow><mo>(</mo><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>+</mo><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>x</mi><mi>x</mi><mi>x</mi></mrow></msub><mo>+</mo><msub><mrow><mrow><mo>(</mo><mi>μ</mi><msup><mrow><mrow><mo>|</mo><mi>ϕ</mi><mo>|</mo></mrow></mrow><mrow><msub><mrow><mi>p</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>−</mo><mn>1</mn></mrow></msup><mi>ϕ</mi><mo>+</mo><msup><mrow><mrow><mo>|</mo><mi>ϕ</mi><mo>|</mo></mrow></mrow><mrow><msub><mrow><mi>p</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>−</mo><mn>1</mn></mrow></msup><mi>ϕ</mi><mo>)</mo></mrow></mrow><mrow><mi>x</mi></mrow></msub><mo>)</mo></mrow></mrow><mrow><mi>x</mi></mrow></msub><mo>=</mo><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>y</mi><mi>y</mi></mrow></msub><mo>,</mo></mrow></math></span></span></span>where <span><math><mrow><mi>μ</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span>. When <span><math><mrow><mn>1</mn><mo>&lt;</mo><msub><mrow><mi>p</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>&lt;</mo><msub><mrow><mi>p</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>&lt;</mo><mfrac><mrow><mn>7</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mrow></math></span>, we show that the set of solitary wave solutions is orbitally stable by using variational methods. When <span><math><mrow><mn>1</mn><mo>&lt;</mo><msub><mrow><mi>p</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>&lt;</mo><mfrac><mrow><mn>7</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mrow></math></span> and <span><math><mrow><mn>3</mn><mo>≤</mo><msub><mrow><mi>p</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>&lt;</mo><mn>5</mn></mrow></math></span>, we establish that all energy minimizers correspond to local minima of the associated energy functional and then the set of energy minimizers is orbitally stable. Furthermore, we show that the solitary waves are strongly unstable in the case of <span><math><mrow><mn>3</mn><mo>≤</mo><msub><mrow><mi>p</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>&lt;</mo><msub><mrow><mi>p</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>&lt;</mo><mn>5</mn></mrow></math></span> by blow-up. Our main results improve and complement the existing results in the literature recently.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"482 ","pages":"Article 134875"},"PeriodicalIF":2.9,"publicationDate":"2025-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144858486","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 of a diffusive two-predator-one-prey model in advective heterogeneous environments","authors":"Li Ma ,&nbsp;De Tang ,&nbsp;Lulu Tong","doi":"10.1016/j.physd.2025.134867","DOIUrl":"10.1016/j.physd.2025.134867","url":null,"abstract":"<div><div>In this paper, we investigate the dynamics and asymptotic profiles of positive steady states of a general diffusive two-predator-one-prey model in advective heterogeneous environments. By the abstract persistence theory, the system is uniformly persistent under some assumptions, regardless of how the diffusion and advection rates vary. Furthermore, we analyze the role of advection on the limiting profiles of positive steady states. Our findings show that as the advection parameter varies, the limiting profile of positive steady states becomes very complicated, including multiple scenarios: coexistence (with multiple solutions) and extinction of the three species under different conditions. Finally, we demonstrate the correctness of the theoretical results and find some interesting phenomena through some numerical simulations.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134867"},"PeriodicalIF":2.9,"publicationDate":"2025-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144830993","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":"Bound states of temporal Kerr solitons mediated by pump depletion in a doubly resonant optical parametric oscillator","authors":"Brahim Baydi ,&nbsp;Majid Taki ,&nbsp;François Leo ,&nbsp;Saliya Coulibaly ,&nbsp;Carlos Mas Arabí","doi":"10.1016/j.physd.2025.134873","DOIUrl":"10.1016/j.physd.2025.134873","url":null,"abstract":"<div><div>We theoretically study the interaction between two parametrically driven Kerr cavity solitons in a doubly resonant optical parametric oscillator. In the presence of weak walk-off, the depletion dynamics induce oscillating tails in the temporal profile of the pump, leading to the formation of bound states. Our study reveals the critical role of walk-off and depletion effects in governing the long-range interaction and binding mechanisms between solitons, offering new insights into the control and stabilization of soliton pairs in parametric systems.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"482 ","pages":"Article 134873"},"PeriodicalIF":2.9,"publicationDate":"2025-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144864478","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 the conservation of helicity by weak solutions of the 3D Euler and inviscid MHD equations","authors":"Daniel W. Boutros ,&nbsp;Edriss S. Titi","doi":"10.1016/j.physd.2025.134876","DOIUrl":"10.1016/j.physd.2025.134876","url":null,"abstract":"<div><div>Classical solutions of the three-dimensional Euler equations of an ideal incompressible fluid conserve the helicity. We introduce a new weak formulation of the vorticity formulation of the Euler equations in which (by implementing the Bony paradifferential calculus) the advection terms are interpreted as paraproducts for weak solutions with low regularity. Using this approach we establish an equation of local helicity balance, which gives a rigorous foundation to the concept of local helicity density and flux at low regularity. We provide a sufficient criterion for helicity conservation which is weaker than many of the existing sufficient criteria for helicity conservation in the literature.</div><div>Subsequently, we prove a sufficient condition for the helicity to be conserved in the zero viscosity limit of the Navier–Stokes equations. Moreover, we establish a relation between the defect measure (which is part of the local helicity balance) and a third-order structure function for solutions of the Euler equations. As a byproduct of the approach introduced in this paper, we also obtain a new sufficient condition for the conservation of magnetic helicity in the inviscid MHD equations, as well as for the kinematic dynamo model.</div><div>Finally, it is known that classical solutions of the ideal (inviscid) MHD equations which have divergence-free initial data will remain divergence-free, but this need not hold for weak solutions. We show that weak solutions of the ideal MHD equations arising as weak-<span><math><mo>∗</mo></math></span> limits of Leray–Hopf weak solutions of the viscous and resistive MHD equations remain divergence-free in time.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134876"},"PeriodicalIF":2.9,"publicationDate":"2025-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144830998","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":"Complex structure of time-periodic solutions decoded in Poincaré–Lindstedt series: The cubic conformal wave equation on S3","authors":"Filip Ficek ,&nbsp;Maciej Maliborski","doi":"10.1016/j.physd.2025.134864","DOIUrl":"10.1016/j.physd.2025.134864","url":null,"abstract":"<div><div>This work explores the rich structure of spherically symmetric time-periodic solutions of the cubic conformal wave equation on <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>. We discover that the families of solutions bifurcating from the eigenmodes of the linearized equation form patterns similar to the ones observed for the cubic wave equation. Alongside the Galerkin approaches, we study them using the new method based on the Padé approximants. To do so, we provide a rigorous perturbative construction of solutions. Due to the conformal symmetry, the solutions presented in this work serve as examples of large time-periodic solutions of the conformally coupled scalar field on the anti-de Sitter background.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134864"},"PeriodicalIF":2.9,"publicationDate":"2025-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144830991","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 of dark and bright solitons in the discrete nonlinear Schrödinger equation","authors":"F.T. Adriano ,&nbsp;A.N. Hasmi ,&nbsp;R. Kusdiantara ,&nbsp;H. Susanto","doi":"10.1016/j.physd.2025.134848","DOIUrl":"10.1016/j.physd.2025.134848","url":null,"abstract":"<div><div>We investigate the existence and linear stability of solitons in the nonlinear Schrödinger lattices in the strong coupling regime. Focusing and defocusing nonlinearities are considered, giving rise to bright and dark solitons. In this regime, the effects of lattice discreteness become exponentially small, requiring a beyond-all-orders analysis. To this end, we employ exponential asymptotics to derive soliton solutions and examine their stability systematically. We show that only two symmetry-related soliton configurations are permissible: onsite solitons centered at lattice sites and intersite solitons positioned between adjacent sites. Although the instability of intersite solitons due to real eigenvalue pairs is known numerically, a rigorous analytical account, <em>particularly for dark solitons</em>, has been lacking. Our work fills this gap, yielding analytical predictions that match numerical computations with high accuracy. We also establish the linear stability of onsite bright solitons. While the method cannot directly resolve the quartet eigenvalue-induced instability of onsite dark solitons due to the continuous spectrum covering the entire imaginary axis, we conjecture an eigenvalue-counting argument that supports their instability. Overall, our application of the exponential asymptotics method shows the versatility of this approach for addressing multiscale problems in discrete nonlinear systems.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134848"},"PeriodicalIF":2.9,"publicationDate":"2025-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144809601","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":"Elastic interaction of counter-propagating waves of arbitrary amplitude on the surface of a magnetic fluid in a tangential magnetic field in 3D geometry","authors":"Nikolay M. Zubarev ,&nbsp;Olga V. Zubareva","doi":"10.1016/j.physd.2025.134885","DOIUrl":"10.1016/j.physd.2025.134885","url":null,"abstract":"<div><div>The propagation of nonlinear waves on the initially flat free surface of a magnetic fluid subjected to a strong uniform tangential magnetic field is investigated. For fluids with high magnetic permeability, boundary perturbations of arbitrary shape can propagate undistorted both in the direction of the applied field and against it. We demonstrate that the interaction between counter-propagating spatially localized waves is elastic, i.e., they conserve energy and momentum during collisions. This result is exact: it has been derived for the three-dimensional geometry of the system, with no restrictions on the amplitude of surface waves.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134885"},"PeriodicalIF":2.9,"publicationDate":"2025-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144830996","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":"Cut-offs in a degenerate advection–reaction–diffusion equation — a case study","authors":"Nikola Popović ,&nbsp;Mariya Ptashnyk ,&nbsp;Zak Sattar","doi":"10.1016/j.physd.2025.134870","DOIUrl":"10.1016/j.physd.2025.134870","url":null,"abstract":"<div><div>We investigate the effect of a Heaviside cut-off on the front propagation dynamics of a degenerate advection–reaction–diffusion equation. In particular, we consider two formulations of the equation, one with the cut-off function multiplying the reaction kinetics alone and one in which the cut-off is also applied to the advection term. We prove the existence and uniqueness of a “critical” front solution in both cases, and we derive the leading-order correction to the front propagation speed in dependence on the advection strength and the cut-off parameter. We show that, while the asymptotics of the correction in the cut-off parameter remains unchanged to leading order when the advection term is cut off, the corresponding coefficient is different. Finally, we consider a generalised family of advection–reaction–diffusion equations, and we identify scenarios in which the application of a cut-off to the advection term substantially affects the front propagation speed. Our analysis relies on geometric techniques from dynamical systems theory and, specifically, on geometric desingularisation, also known as “blow-up”.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"482 ","pages":"Article 134870"},"PeriodicalIF":2.9,"publicationDate":"2025-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144864477","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":"Slushball Earth equilibria in a one-dimensional energy balance model","authors":"Aksel Samuelsberg,&nbsp;Per Kristen Jakobsen","doi":"10.1016/j.physd.2025.134866","DOIUrl":"10.1016/j.physd.2025.134866","url":null,"abstract":"<div><div>Understanding the widespread glaciations of the late Neoproterozoic era (715–635 Ma) is important for understanding the evolution of life on Earth. A Waterbelt state has been proposed as a more biologically friendly alternative to the Snowball Earth hypothesis. It was subsequently shown that an open tropical ocean can be sustained by a so-called “Jormungand mechanism”, where darker, bare sea ice at the descending edge of the Hadley cell halts the runaway ice-albedo feedback synonymous with Snowball Earth. However, the geological evidence for thick, active glaciers at sea level in the deep tropics during these glaciations presents a problem for the Waterbelt hypothesis that has received limited attention in the literature. We study a diffusive, one-dimensional energy balance model (EBM) with a Jormungand mechanism, where also the effects at the ascending edge of the Hadley cell are included. The EBM is solved using an analytical approach, the boundary integral method. The modified Jormungand mechanism produces several unstable Slushball Earth states in the EBM, in addition to the Waterbelt states. These Slushball Earth states are similar to Snowball Earth, but with a series of water belts over lower latitudes. Implications for the Neoproterozoic glaciations are discussed.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"482 ","pages":"Article 134866"},"PeriodicalIF":2.9,"publicationDate":"2025-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144887063","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}