27 citations · 44 across the 6 of their papers we have counts for
7 papers
Computation of Large-Genus Solutions of the Korteweg-de Vries Equation
Deniz Bilman, Patrik Nabelek, Thomas Trogdon
We consider the numerical computation of finite-genus solutions of the Korteweg-de Vries equation when the genus is large. Our method applies both to the initial-value problem when…
Distributions Supported on Fractal Sets and Solutions to the Kadomtsev--Petviashvili Equation
Patrik V. Nabelek
In this note we will discuss a potentially interesting extension of some recent results on primitive solutions to completely integrable partial differential equations. We will disc…
Cluster Strong Lensing with Hierarchical Inference
Pietro Bergamini, Adriano Agnello, Gabriel Bartosch Caminha
Lensing by galaxy clusters is a versatile probe of cosmology and extragalactic astrophysics, but the accuracy of some of its predictions is limited by the simplified models adopted…
Solutions to the Kaup--Broer System and Its 2+1 Dimensional Integrable Generalization via the Dressing Method
Patrik V. Nabelek, Vladimir E. Zakharov
In this paper we formulate the nonlocal dbar problem dressing method of Manakov and Zakharov [28, 29, 27] for the 4 scaling classes of the 1+1 dimensional Kaup--Broer system [7, 13…
Algebro-Geometric Finite Gap Solutions to the Korteweg--de Vries Equation as Primitive Solutions
Patrik V. Nabelek
In this paper we show that all algebro-geometric finite gap solutions to the Korteweg--de Vries equation can be realized as a limit of N-soliton solutions as N diverges to infinity…
On symmetric primitive potentials
Patrik Nabelek, Dmitry Zakharov, Vladimir Zakharov
The concept of a primitive potential for the Schroedinger operator on the line was introduced in [2,3,4]. Such a potential is determined by a pair of positive functions on a finite…
A Riemann--Hilbert Problem Approach to Periodic Infinite Gap Hill's Operators and the Korteweg--de Vries Equation
Kenneth T-R. McLaughlin, Patrik V. Nabelek
We formulate the inverse spectral theory of infinite gap Hill's operators with bounded periodic potential as a Riemann--Hilbert problem on a typically infinite collection of spectr…