Results 51 to 60 of about 39,546 (135)
Visnik Harkivsʹkogo Nacionalʹnogo Universitetu im. V.N. Karazina. Cepiâ Matematika, Prikladna Matematika i Mehanika, 2018 We study the Cauchy problem for the integrable nonlocal nonlinear Schr\"odinger (NNLS) equation \[ iq_{t}(x,t)+q_{xx}(x,t)+2 q^{2}(x,t)\bar{q}(-x,t)=0 \] with a step-like initial data: $q(x,0)=o(1)$ as $x\to-\infty$ and $q(x,0)=A+o(1)$ as $x\to\infty ...
Ya. Rybalko, D. G. Shepelsky
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Fortschritte der Physik, Volume 74, Issue 4, April 2026.ABSTRACT In this paper, we continue the development of the Cartan neural networks programme, launched with three previous publications, by focusing on some mathematical foundational aspects that we deem necessary for our next steps forward. The mathematical and conceptual results are diverse and span various mathematical fields, but the inspiring ...
Pietro Fré +4 more
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Impact of Quantum Gravity on the UV Sensitivity of Extremal Black Holes
Fortschritte der Physik, Volume 74, Issue 4, April 2026.ABSTRACT Recent work has revealed that extremal Kerr black holes may exhibit a sensitivity to higher‐derivative corrections to Einstein's equations, displaying singularities in the tidal forces at the horizon. However, in a purely gravitational context, this “ultraviolet sensitivity” translates into a strong dependence on the Wilson coefficients in the
Francesco Del Porro +2 more
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Nuclear Physics BIn this paper, we investigate the space-time shifted nonlocal derivative nonlinear Schrödinger (DNLS) equation under nonzero boundary conditions using the Riemann–Hilbert (RH) approach for the first time.
Xin-Yu Liu, Rui Guo
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The Linearized Korteweg–de Vries Equation on the Line With Metric Graph Defects
Studies in Applied Mathematics, Volume 156, Issue 4, April 2026.ABSTRACT We study the small‐amplitude linearization of the Korteweg–de Vries equation on the line with a local defect scattering waves represented by a metric graph domain adjoined at one point. For a representative collection of examples, we derive explicit solution formulas expressed as contour integrals and obtain existence and unicity results for ...
D. A. Smith
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Reductions of Multicomponent mKdV Equations on Symmetric Spaces of DIII-Type
Symmetry, Integrability and Geometry: Methods and Applications, 2008 New reductions for the multicomponent modified Korteweg-de Vries (MMKdV) equations on the symmetric spaces of {f DIII}-type are derived using the approach based on the reduction group introduced by A.V. Mikhailov.
Nikolay A. Kostov, Vladimir S. Gerdjikov
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Mathematika, Volume 72, Issue 2, April 2026.Abstract We establish the connection between the Steinitz problem for ordering vector families in arbitrary norms and its variant for not necessarily zero‐sum families consisting of “nearly unit” vectors.
Gergely Ambrus, Rainie Heck
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Biases towards the zero residue class for quadratic forms in arithmetic progressions
Mathematika, Volume 72, Issue 2, April 2026.Abstract We prove a bias towards the zero residue class in the distribution of the integers represented by binary quadratic forms. In most cases, we prove that the bias comes from a secondary term in an associated asymptotic expansion. This is unlike Chebyshev's bias, which exists somewhere at the level of O(x1/2+ε)$O(x^{1/2+\varepsilon })$.
Jeremy Schlitt
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Graph potentials and topological quantum field theories
Proceedings of the London Mathematical Society, Volume 132, Issue 4, April 2026.Abstract We introduce a new functional equation in birational geometry, whose solutions can be used to construct two‐dimensional topological quantum field theories (2d TQFTs), infinite‐dimensional in many interesting examples. The solutions of the equation give rise to a hierarchy of graph potentials, which, in the simplest setup, are Laurent ...
Pieter Belmans +2 more
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Properties of Matrix Orthogonal Polynomials via their Riemann-Hilbert Characterization
Symmetry, Integrability and Geometry: Methods and Applications, 2011 We give a Riemann-Hilbert approach to the theory of matrix orthogonal polynomials. We will focus on the algebraic aspects of the problem, obtaining difference and differential relations satisfied by the corresponding orthogonal polynomials.
F. Alberto Grünbaum +2 more
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