Results 31 to 40 of about 2,221 (63)

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., Bulla W., Gerald Teschl, Gohberg I., Its A. R., Its A. R., Its A. R., Krüger H., Manakov S. V., Muskhelishvili N. I., Novokshenov V. Yu., Prössdorf S., Spyridon Kamvissis, Stein E. M., Teschl G., Teschl G., Zakharov V. E., Šabat A. B.   +17 more
core   +9 more sources

Numerical Approaches in Nonlinear Fourier Transform‐Based Signal Processing for Telecommunications

Studies in Applied Mathematics, Volume 154, Issue 1, January 2025.
ABSTRACT We discuss applications of the inverse scattering transform, also known as the nonlinear Fourier transform (NFT) in telecommunications, both for nonlinear optical fiber communication channel equalization and time‐domain signal processing techniques.
Egor Sedov, Igor Chekhovskoy, Mikhail Fedoruk, Sergey Turitsyn   +3 more
wiley   +1 more source

Initial-boundary value problems for discrete evolution equations: discrete linear Schrodinger and integrable discrete nonlinear Schrodinger equations

, 2008
We present a method to solve initial-boundary value problems for linear and integrable nonlinear differential-difference evolution equations. The method is the discrete version of the one developed by A. S.
Ablowitz M J, Ablowitz M J, Ablowitz M J, Adler V, Belokolos E D, Bikbaev R F, Calogero F, de Monvel A Boutet, Ehrenpreis L, Faddeev L D, Fokas A S, Gino Biondini, Guenbo Hwang, Henkin G, Manakov S V, Manakov S V, Maruno K-I, Palamodov V P, Sabatier P C, Skylanin E K, Vekslerchik V E, Zakharov V E, Zakharov V E   +22 more
core   +2 more sources

Hypercomplex operator calculus for the fractional Helmholtz equation

Mathematical Methods in the Applied Sciences, Volume 47, Issue 14, Page 11439-11472, 30 September 2024.
In this paper, we develop a hypercomplex operator calculus to treat fully analytically boundary value problems for the homogeneous and inhomogeneous fractional Helmholtz equation where fractional derivatives in the sense of Caputo and Riemann–Liouville are applied.
Nelson Vieira, Milton Ferreira, M. Manuela Rodrigues, Rolf Sören Kraußhar   +3 more
wiley   +1 more source

Dispersive shock waves in the Kadomtsev-Petviashvili and Two Dimensional Benjamin-Ono equations

, 2015
Dispersive shock waves (DSWs) in the Kadomtsev-Petviashvili (KP) equation and two dimensional Benjamin-Ono (2DBO) equation are considered using parabolic front initial data.
Ablowitz, Mark J., Demirci, Ali, Ma, Yi-Ping   +2 more
core   +1 more source

Multidomain spectral approach to rational‐order fractional derivatives

Studies in Applied Mathematics, Volume 152, Issue 4, Page 1110-1132, May 2024.
Abstract We propose a method to numerically compute fractional derivatives (or the fractional Laplacian) on the whole real line via Riesz fractional integrals. The compactified real line is divided into a number of intervals, thus amounting to a multidomain approach; after transformations in accordance with the underlying Zq$Z_{q}$ curve ensuring ...
Christian Klein, Nikola Stoilov
wiley   +1 more source

Designing universal causal deep learning models: The geometric (Hyper)transformer

Mathematical Finance, Volume 34, Issue 2, Page 671-735, April 2024.
Abstract Several problems in stochastic analysis are defined through their geometry, and preserving that geometric structure is essential to generating meaningful predictions. Nevertheless, how to design principled deep learning (DL) models capable of encoding these geometric structures remains largely unknown.
Beatrice Acciaio, Anastasis Kratsios, Gudmund Pammer   +2 more
wiley   +1 more source

The forbidden region for random zeros: Appearance of quadrature domains

Communications on Pure and Applied Mathematics, Volume 77, Issue 3, Page 1766-1849, March 2024.
Abstract Our main discovery is a surprising interplay between quadrature domains on the one hand, and the zeros of the Gaussian Entire Function (GEF) on the other. Specifically, consider the GEF conditioned on the rare hole event that there are no zeros in a given large Jordan domain.
Alon Nishry, Aron Wennman
wiley   +1 more source

Miura transformation for the “good” Boussinesq equation

Studies in Applied Mathematics, Volume 152, Issue 1, Page 73-110, January 2024.
Abstract It is well known that each solution of the modified Korteveg–de Vries (mKdV) equation gives rise, via the Miura transformation, to a solution of the Korteveg–de Vries (KdV) equation. In this work, we show that a similar Miura‐type transformation exists also for the “good” Boussinesq equation.
C. Charlier, J. Lenells
wiley   +1 more source

The Inverse Spectral Transform for the Dunajski hierarchy and some of its reductions, I: Cauchy problem and longtime behavior of solutions

, 2015
In this paper we apply the formal Inverse Spectral Transform for integrable dispersionless PDEs arising from the commutation condition of pairs of one-parameter families of vector fields, recently developed by S. V. Manakov and one of the authors, to one
Santini, P. M., Yi, G.
core   +1 more source