Dispersion Estimates for One-dimensional Discrete Schr\"odinger and Wave Equations [PDF]
, 2015 We derive dispersion estimates for solutions of the one-dimensional discrete perturbed Schr\"odinger and wave equations. In particular, we improve upon previous works and weaken the conditions on the potentials.
Egorova, Iryna +2 more
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On the asymptotics of solutions of Volterra integral equations
Arkiv för Matematik, 1985 Consider the complex-valued, linear Volterra equation \[ (*)\quad v(t)- \int^{t}_{t_ 0}G(t,\tau)v(\tau)d\tau =v_ 0(t),\quad t\geq t_ 0. \] It is known that the solution of this equation can be expressed in terms of a variation of constants formula \[ v(t)=v_ 0(t)- \int^{t}_{t_ 0}R(t,\tau)v_ 0(\tau)d\tau,\quad t\geq t_ 0, \] where R often is called the ...
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Asymptotics of a Class of Solutions to the Cylindrical Toda Equations
, 1997 The small t asymptotics of a class of solutions to the 2D cylindrical Toda equations is computed. The solutions, q_k(t), have the representation q_k(t) = log det(I-lambda K_k) - log det(I-lambda K_{k-1}) where K_k are integral operators.
Tracy, C. A., Widom, H.
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Complete minimal form factors for irrelevant deformations of integrable quantum field theory
Nuclear Physics BIn this paper, we present a method to compute the minimal form factors (MFFs) of diagonal integrable field theories perturbed by generalized TT¯ perturbations.
Fabio Sailis +2 more
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Asymptotics of the solution to a singularly perturbed integral equation
Applied Mathematics Letters, 1991 AbstractThe leading term of the asymptotics as ϵ → +0 of the solution to the equation ϵhϵ+ ∫1-1exp(-a∣x-u∣)hϵ(y)dy=f(x),-1≤x≤1,fϵC4(-1,1) is calculated.
Alexander G. Ramm, E.I. Shifrin
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Asymptotic behavior of solutions to nonlinear Volterra integral equations
Journal of Mathematical Analysis and Applications, 1984 Die Autoren untersuchen das asymptotische Verhalten für \(t\to \infty\) von Lösungen der nichtlinearen Volterra-Integralgleichung \[ \quad u(t)+\int^{t}_{0}b(t-s)Au(s)ds\ni F(t),\quad t\geq 0, \] wobei A ein abgeschlossener nichtlinearer akkretiver Operator in einem Banachraum ist.
Douglas S Hulbert, Simeon Reich
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New formulas for Maslov's canonical operator in a neighborhood of focal points and caustics in 2D semiclassical asymptotics [PDF]
, 2013 We suggest a new representation of Maslov’s canonical operator in a neighborhood of caustics using a special class of coordinate systems (eikonal coordinates) on Lagrangian manifolds.
Dobrokhotov, S.Yu. +3 more
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Moment inequalities and high-energy tails for the Boltzmann equations with inelastic interactions
, 2003 We study the high-energy asymptotics of the steady velocity distributions for model systems of granular media in various regimes. The main results obtained are integral estimates of solutions of the hard-sphere Boltzmann equations, which imply that the ...
Bobylev, Alexander V. +2 more
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Stability of the periodic Toda lattice under short range perturbations [PDF]
, 2011 We consider the stability of the periodic Toda lattice (and slightly more generally of the algebro-geometric finite-gap lattice) under a short range perturbation. We prove that the perturbed lattice asymptotically approaches a modulated lattice.
Ablowitz M. J. +17 more
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Periodic and asymptotically periodic solutions of neutral integral equations
Proceedings of The 6'th Colloquium on the Qualitative Theory of Differential Equations (August 10--14, 1999, Szeged, Hungary) edited by: Géza Makay and László Hatvani, 1999 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Tetsuo Furumochi, Theodore Burton
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