Results 51 to 60 of about 552 (182)
Fractal and Fractional, 2022 It is well known that multicomponent integrable systems provide a method for analyzing phenomena with numerous interactions, due to the interactions between their different components. In this paper, we derive the multicomponent higher-order Chen–Lee–Liu
Yong Zhang, Huanhe Dong, Yong Fang
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Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.Abstract We study the multiplicative statistics associated to the limiting determinantal point process describing eigenvalues of unitary random matrices with a critical edge point, where the limiting eigenvalue density vanishes like a power 5/2. We prove that these statistics are governed by the first three equations of the Korteweg‐de‐Vries (KdV ...
Mattia Cafasso +1 more
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Riemann–Hilbert problems from Donaldson–Thomas theory [PDF]
Inventiones mathematicae, 2018 We study a class of Riemann-Hilbert problems arising naturally in Donaldson-Thomas theory. In certain special cases we show that these problems have unique solutions which can be written explicitly as products of gamma functions. We briefly explain connections with Gromov-Witten theory and exact WKB analysis.
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The Modified Coupled Hirota Equation: Riemann-Hilbert Approach and N-Soliton Solutions
Abstract and Applied Analysis, 2019 The Cauchy initial value problem of the modified coupled Hirota equation is studied in the framework of Riemann-Hilbert approach. The N-soliton solutions are given in a compact form as a ratio of (N+1)×(N+1) determinant and N×N determinant, and the ...
Siqi Xu
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Discrete analogues of second‐order Riesz transforms
Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.Abstract Discrete analogues of classical operators in harmonic analysis have been widely studied, revealing deep connections with areas such as ergodic theory and analytic number theory. This line of research is commonly known as Discrete Analogues in Harmonic Analysis (DAHA).
Rodrigo Bañuelos, Daesung Kim
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Electronic Journal of Differential Equations, 2013 In the first part of this article, we study a discontinuous Riemann-Hilbert problem for nonlinear uniformly elliptic complex equations of first order in multiply connected domains. First we show its well-posedness. Then we give the representation of
Guo-Chun Wen
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$L_{p;r} $ spaces: Cauchy Singular Integral, Hardy Classes and Riemann-Hilbert Problem in this Framework [PDF]
Sahand Communications in Mathematical Analysis, 2019 In the present work the space $L_{p;r} $ which is continuously embedded into $L_{p} $ is introduced. The corresponding Hardy spaces of analytic functions are defined as well. Some properties of the functions from these spaces are studied.
Ali Huseynli, Asmar Mirzabalayeva
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Convergence properties of dynamic mode decomposition for analytic interval maps
Communications on Pure and Applied Mathematics, Volume 79, Issue 2, Page 179-206, February 2026.Abstract Extended dynamic mode decomposition (EDMD) is a data‐driven algorithm for approximating spectral data of the Koopman operator associated to a dynamical system, combining a Galerkin method with N$N$ functions and a quadrature method with M$M$ quadrature nodes.
Elliz Akindji +3 more
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Lax equations, factorization and Riemann–Hilbert problems
Portugaliae Mathematica, 2007 The paper deals with the problem of existence and calculation of solutions to Lax equations that define finite-dimensional integrable systems. The method presented in the paper is based on Wiener–Hopf factorization and related Riemann–Hilbert problems on Riemann surfaces. The idea behind the method was first proposed by Semenov–Tian–Shansky but, to the
Câmara, M. Cristina +2 more
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Long-Time Asymptotics of a Three-Component Coupled mKdV System
Mathematics, 2019 We present an application of the nonlinear steepest descent method to a three-component coupled mKdV system associated with a 4 × 4 matrix spectral problem. An integrable coupled mKdV hierarchy with three potentials is first generated. Based
Wen-Xiu Ma
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