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Gradient Estimates for a Nonlinear Parabolic Equation Under the Yamabe Flow Yamabe流下非线性抛物方程的梯度估计
IF 1.2 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2026-08-06 DOI: 10.1007/s11040-026-09585-9
Chenlin Huang, Fei Yang
{"title":"Gradient Estimates for a Nonlinear Parabolic Equation Under the Yamabe Flow","authors":"Chenlin Huang,&nbsp;Fei Yang","doi":"10.1007/s11040-026-09585-9","DOIUrl":"10.1007/s11040-026-09585-9","url":null,"abstract":"<div><p>In this paper, we establish gradient estimates for positive solutions to the nonlinear parabolic equation <span>((Delta _phi -partial _t)u=hu^q+au(ln u)^alpha )</span> on a complete Riemannian manifold <span>((M^{n},g))</span>, under a Bakry-Émery Ricci curvature bound along the Yamabe flow. By integrating these gradient estimates, we also obtain the corresponding Harnack inequalities.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"29 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148751066","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}
引用次数: 0
Lie Symmetry Analysis, Conservation Laws and Stability Analysis for the Nonhomogeneous Monge–ampère equation 非齐次monge - ampantre方程的Lie对称性分析、守恒律和稳定性分析
IF 1.2 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2026-08-05 DOI: 10.1007/s11040-026-09575-x
Germán F. Escobar F., Oscar M. Londoño D., Julio C. Duarte V.
{"title":"Lie Symmetry Analysis, Conservation Laws and Stability Analysis for the Nonhomogeneous Monge–ampère equation","authors":"Germán F. Escobar F.,&nbsp;Oscar M. Londoño D.,&nbsp;Julio C. Duarte V.","doi":"10.1007/s11040-026-09575-x","DOIUrl":"10.1007/s11040-026-09575-x","url":null,"abstract":"<div><p>This work presents a symmetry analysis of the nonhomogeneous Monge–Ampère equation <span>(varvec{det D^{2} u = x^{p} y^{q}})</span> in <span>(varvec{Omega subset } pmb {mathbb {R}}^{textbf{2}})</span>, with <span>(varvec{p, q in } pmb {mathbb {R}})</span>. Using Lie group theory, we classify all point symmetries, obtaining a five-dimensional Lie algebra in the generic case, which is solvable and isomorphic to <span>({mathbb {R}}^3 ltimes {mathbb {R}}^2)</span>. We prove the equation is nonlinearly self-adjoint and apply Ibragimov’s theorem to derive explicit conservation laws for each symmetry generator. The adjoint representation of the Lie algebra is constructed, and a one-dimensional optimal system of subalgebras is determined, enabling classification of all distinct symmetry reductions. These reductions yield nonlinear ordinary differential equations, analyzed qualitatively via Poincaré compactification to identify critical points at infinity and their stability. The results provide a comprehensive structural description of the equation’s symmetries, conservation laws, and invariant solutions, enhancing understanding of its geometric and analytical properties.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"29 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11040-026-09575-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148750750","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Gradient Measures on Cayley Trees Associated with Two Periodic Homogeneous and Inhomogeneous Boundary Laws for the SOS Model 基于两个周期齐次和非齐次边界律的Cayley树的梯度测度
IF 1.2 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2026-08-04 DOI: 10.1007/s11040-026-09581-z
R. A. Ilyasova
{"title":"Gradient Measures on Cayley Trees Associated with Two Periodic Homogeneous and Inhomogeneous Boundary Laws for the SOS Model","authors":"R. A. Ilyasova","doi":"10.1007/s11040-026-09581-z","DOIUrl":"10.1007/s11040-026-09581-z","url":null,"abstract":"<div><p>This paper investigates gradient Gibbs measures within the SOS model, obtained via <span>(2)</span>-height periodic boundary laws associated with <span>(G_{k}^{(2)})</span> (<span>(G_{k}^{(2)})</span>-boundary law) on <span>(mathcal {G})</span>-admissible configuration spaces for graphs with infinite symmetric Toeplitz adjacency matrices [2], focusing on Cayley trees of arbitrary order.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"29 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148750644","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}
引用次数: 0
Affine Weyl Groups and Non-Abelian Discrete Systems: An Application to the d-Painlevé Equations 仿射Weyl群与非阿贝尔离散系统：在d- painlevleve方程中的应用
IF 1.2 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2026-08-03 DOI: 10.1007/s11040-026-09573-z
Irina Bobrova
{"title":"Affine Weyl Groups and Non-Abelian Discrete Systems: An Application to the d-Painlevé Equations","authors":"Irina Bobrova","doi":"10.1007/s11040-026-09573-z","DOIUrl":"10.1007/s11040-026-09573-z","url":null,"abstract":"<div><p>A non-abelian generalisation of a birational representation of affine Weyl groups and their application to the discrete dynamical systems is presented. By using this generalisation, non-commutative analogs for the discrete systems of <span>(A_n^{(1)})</span>, <span>(n ge 2)</span> type and of <i>d</i>-Painlevé equations with an additive dynamic were derived. A coalescence cascade of the later is also discussed.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"29 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148750706","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}
引用次数: 0
On the Large-Time Asymptotics of the Defocusing mKdV Equation with Step-Like Initial Data 具有步长初始数据的散焦mKdV方程的大时间渐近性
IF 1.2 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2026-07-28 DOI: 10.1007/s11040-026-09579-7
Taiyang Xu, Yidan Zhang
{"title":"On the Large-Time Asymptotics of the Defocusing mKdV Equation with Step-Like Initial Data","authors":"Taiyang Xu,&nbsp;Yidan Zhang","doi":"10.1007/s11040-026-09579-7","DOIUrl":"10.1007/s11040-026-09579-7","url":null,"abstract":"<div><p>We study the Cauchy problem for the defocusing modified Korteweg–de Vries (mKdV) equation with step-like initial data approaching nonzero constants <span>(c_l)</span> and <span>(c_r)</span> as <span>(x rightarrow -infty )</span> and <span>(xrightarrow +infty )</span>, respectively. Assuming <span>(c_l&gt;c_r&gt;0)</span>, the solution exhibits a rarefaction wave structure. We first develop the inverse scattering transform for the solution satisfying these step-like boundary conditions. Using the associated scattering data, we prove that there exists a unique global solution of the Cauchy problem and characterize it in terms of a Riemann–Hilbert (RH) problem. By applying the nonlinear steepest descent method to this RH problem, we rigorously obtain large-time asymptotics of rarefaction wave solution in three distinct space-time regions, each characterized by a different leading order behavior. They are: (I) a left-field region where the solution approaches the left background constant, modulo a small oscillatory correction, (II) a central region where the solution exhibits a slowly varying profile that transitions between the two constants, and (III) a right-field region where the solution tends to the right background constant, up to an algebraically small correction. Rigorous derivations of the leading terms, sub-leading terms as well as the error bounds are presented.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"29 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148614458","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}
引用次数: 0
Decoupling and Decay of Two-Point Functions in a Two-Species (T)ASEP 二种(T)ASEP中两点函数的解耦与衰减
IF 1.2 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2026-07-28 DOI: 10.1007/s11040-026-09580-0
Patrik L. Ferrari, Sabrina Gernholt
{"title":"Decoupling and Decay of Two-Point Functions in a Two-Species (T)ASEP","authors":"Patrik L. Ferrari,&nbsp;Sabrina Gernholt","doi":"10.1007/s11040-026-09580-0","DOIUrl":"10.1007/s11040-026-09580-0","url":null,"abstract":"<div><p>We consider the two-species totally asymmetric simple exclusion process on <span>(mathbb {Z})</span> with a translation-invariant stationary measure as the initial condition. We establish the asymptotic decoupling of the marginal height profiles along characteristic lines and prove the decay of the two-point functions in the large-time limit, thus confirming predictions of the nonlinear fluctuating hydrodynamics theory. Our approach builds on the queueing construction of the stationary measure introduced in [7, 32] and extends the theory of backwards paths for height functions developed in [14, 35]. The arguments for asymptotic decoupling also apply to further homogeneous initial data, and the decay of the two-point functions is proven for the stationary two-species asymmetric simple exclusion process, beyond the totally asymmetric case.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"29 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11040-026-09580-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148614979","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Correction: Locations of JNR Skyrmions 更正：JNR skyrmins的位置
IF 1.2 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2026-07-22 DOI: 10.1007/s11040-026-09577-9
Josh Cork, Linden Disney-Hogg
{"title":"Correction: Locations of JNR Skyrmions","authors":"Josh Cork,&nbsp;Linden Disney-Hogg","doi":"10.1007/s11040-026-09577-9","DOIUrl":"10.1007/s11040-026-09577-9","url":null,"abstract":"","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"29 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11040-026-09577-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148613606","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Scaling Relations for the CLG’s Critical Exponents CLG临界指数的标度关系
IF 1.2 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2026-07-21 DOI: 10.1007/s11040-026-09578-8
Clément Erignoux, Assaf Shapira, Marielle Simon
{"title":"Scaling Relations for the CLG’s Critical Exponents","authors":"Clément Erignoux,&nbsp;Assaf Shapira,&nbsp;Marielle Simon","doi":"10.1007/s11040-026-09578-8","DOIUrl":"10.1007/s11040-026-09578-8","url":null,"abstract":"<div><p>We consider, in any dimension, a constrained lattice gas introduced by physicists [1], which is an exclusion process on a <i>d</i>-dimensional lattice following the additional constraint that only particles with at least one occupied neighbour can jump. In dimension <span>(dge 2)</span>, this model features self-organized criticality at some critical density of particles. Numerical simulations predict the existence of scaling exponents close to criticality, and several relations can be derived between these exponents. The goal of this article is to give a mathematical framework for these relations, which have been numerically established in a companion article [2].</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"29 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148613725","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}
引用次数: 0
Discrete Equations from BäckLund Transformations of the Fifth Painlevé Equation 离散方程BäckLund第五阶painlev<e:1>方程的变换
IF 1.2 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2026-07-16 DOI: 10.1007/s11040-026-09571-1
Peter A. Clarkson, Clare Dunning, Ben Mitchell
{"title":"Discrete Equations from BäckLund Transformations of the Fifth Painlevé Equation","authors":"Peter A. Clarkson,&nbsp;Clare Dunning,&nbsp;Ben Mitchell","doi":"10.1007/s11040-026-09571-1","DOIUrl":"10.1007/s11040-026-09571-1","url":null,"abstract":"<div><p>In this paper discrete equations are derived from Bäcklund transformations of the fifth Painlevé equation, including a new discrete equation which has ternary symmetry. There are two classes of rational solutions of the fifth Painlevé equation, one expressed in terms of the generalised Laguerre polynomials and the other in terms of the generalised Umemura polynomials, both of which can be expressed as Wronskians of Laguerre polynomials. Hierarchies of rational solutions of the discrete equations are derived in terms of the generalised Laguerre and generalised Umemura polynomials. It is known that there is non-uniqueness of some rational solutions of the fifth Painlevé equation. Pairs of non-unique rational solutions are used to derive distinct hierarchies of rational solutions which satisfy the same discrete equation.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"29 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11040-026-09571-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148466389","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Discrete Integrable Systems Associated with Orthogonal Polynomials on Algebraic Curves 代数曲线上与正交多项式相关的离散可积系统
IF 1.2 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2026-07-11 DOI: 10.1007/s11040-026-09572-0
Jing-Rui Wu, Xing-Biao Hu
{"title":"Discrete Integrable Systems Associated with Orthogonal Polynomials on Algebraic Curves","authors":"Jing-Rui Wu,&nbsp;Xing-Biao Hu","doi":"10.1007/s11040-026-09572-0","DOIUrl":"10.1007/s11040-026-09572-0","url":null,"abstract":"<div><p>We extend the integrability framework originally introduced by Spicer, Nijhoff, and van der Kamp by reformulating it in terms of two real variables defined on the unit circle. This geometric perspective is then generalized to other algebraic curves, specifically, the Folium of Descartes and Viviani’s curve. Within this extended setting, we apply determinant identities to orthogonal polynomials and employ Christoffel and Geronimus transformations to construct discrete integrable systems associated with these curves. For each curve, we derive corresponding Lax pairs and matrix representations, highlighting the underlying symmetry and algebraic structure. The unit-circle case is closely related to the higher analogue of the discrete-time Toda equation (HADT) and the quotient-quotient-difference (QQD) scheme, while the systems associated with the Folium of Descartes and Viviani’s curve appear to provide new examples within the present framework. Our results illustrate how algebraic geometry and orthogonal polynomial theory can be effectively combined to construct discrete integrable dynamics, offering promising directions for further exploration in discrete integrability and geometric methods in mathematical physics.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"29 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148465619","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}
引用次数: 0
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