[图书][B] Riemann–Hilbert problems, their numerical solution, and the computation of nonlinear special functions
This book grew out of the collaboration of the authors, which began in the Spring of 2010,
and the first author's PhD dissertation. The second author developed much of the theory in …
and the first author's PhD dissertation. The second author developed much of the theory in …
Extreme superposition: rogue waves of infinite order and the Painlevé-III hierarchy
We study the fundamental rogue wave solutions of the focusing nonlinear Schrödinger
equation in the limit of large order. Using a recently proposed Riemann–Hilbert …
equation in the limit of large order. Using a recently proposed Riemann–Hilbert …
Inverse scattering transform for nonlinear Schrödinger systems on a nontrivial background: a survey of classical results, new developments and future directions
B Prinari - Journal of Nonlinear Mathematical Physics, 2023 - Springer
In this topical review paper we provide a survey of classical and more recent results on the
IST for one-dimensional scalar, vector and square matrix NLS systems on the line (-∞< …
IST for one-dimensional scalar, vector and square matrix NLS systems on the line (-∞< …
Fast algorithms using orthogonal polynomials
We review recent advances in algorithms for quadrature, transforms, differential equations
and singular integral equations using orthogonal polynomials. Quadrature based on …
and singular integral equations using orthogonal polynomials. Quadrature based on …
[HTML][HTML] Phase computation for the finite-genus solutions to the focusing nonlinear Schrödinger equation using convolutional neural networks
We develop a method for retrieving a set of parameters of a quasi-periodic finite-genus
(finite-gap) solution to the focusing nonlinear Schrödinger (NLS) equation, given the solution …
(finite-gap) solution to the focusing nonlinear Schrödinger (NLS) equation, given the solution …
Fast computation of Gauss quadrature nodes and weights on the whole real line
A fast and accurate algorithm for the computation of Gauss–Hermite and generalized Gauss–
Hermite quadrature nodes and weights is presented. The algorithm is based on Newton's …
Hermite quadrature nodes and weights is presented. The algorithm is based on Newton's …
Utilization of the ExactMPF package for solving a discrete analogue of the nonlinear Schrödinger equation by the inverse scattering transform method
VM Adukov, G Mishuris - Proceedings of the Royal …, 2023 - royalsocietypublishing.org
We are revisiting the problem of solving a discrete nonlinear Schrödinger equation by the
inverse scattering transform method, by use of the recently developed ExactMPF package …
inverse scattering transform method, by use of the recently developed ExactMPF package …
A fast, simple, and stable Chebyshev--Legendre transform using an asymptotic formula
N Hale, A Townsend - SIAM Journal on Scientific Computing, 2014 - SIAM
A fast, simple, and numerically stable transform for converting between Legendre and
Chebyshev coefficients of a degree N polynomial in O(N(\logN)^2/\log\logN) operations is …
Chebyshev coefficients of a degree N polynomial in O(N(\logN)^2/\log\logN) operations is …
Numerical inverse scattering transform for the focusing and defocusing Kundu–Eckhaus equations
S Cui, Z Wang - Physica D: Nonlinear Phenomena, 2023 - Elsevier
In this paper, we develop the numerical inverse scattering transform (NIST) for the focusing
and defocusing Kundu–Eckhaus (KE) equations. The NIST consists of numerical direct …
and defocusing Kundu–Eckhaus (KE) equations. The NIST consists of numerical direct …
Numerical inverse scattering for the Korteweg–de Vries and modified Korteweg–de Vries equations
Recent advances in the numerical solution of Riemann–Hilbert problems allow for the
implementation of a Cauchy initial-value problem solver for the Korteweg–de Vries equation …
implementation of a Cauchy initial-value problem solver for the Korteweg–de Vries equation …