Related papers: Nonlocal massive Thirring model and its solutions
Many practical approximations in physics and engineering invoke a relatively long physical domain with a relatively thin cross-section. In this scenario we typically expect the system to have structures that vary slowly in the long…
In this work, we shall investigate existence and multiplicity of solutions for a nonlocal elliptic systems driven by the fractional Laplacian. Specifically, we establish the existence of two positive solutions for following class of…
We construct exact soliton solutions of integrable multicomponent nonlinear Schr\"odinger (NLS) equations under general nonvanishing boundary conditions. Different components of the vector (or matrix) dependent variable can approach plane…
In this letter we propose an approach to obtain solutions for the nonlocal nonlinear Schr\"{o}dinger hierarchy from the known ones of the Ablowitz-Kaup-Newell-Segur hierarchy by reduction. These solutions are presented in terms of double…
A local convergence analysis of the Gauss-Newton method for solving injective-overdetermined systems of nonlinear equations under a majorant condition is provided. The convergence as well as results on its rate are established without a…
Recently a variety of nonlocal integrable systems has been introduced that besides fields located at particlar space-time points simultaneously also contain fields that are located at different, but symmetrically related, points. Here we…
The aim of this paper is to develop the inverse scattering transform (IST) for multi-component generalisations of nonlocal reductions of the nonlinear Schrodinger (NLS) equation with PT-symmetry related to symmetric spaces. This includes:…
In this work we present a variant of the fast multipole method (FMM) for efficiently evaluating standard layer potentials on geometries with complex coordinates in two and three dimensions. The complex scaled boundary integral method for…
A challenge in the theory of integrable systems is to show for every nonultralocal quantum integrable model, a possible connection to an ultralocal model. Some of such gauge connections were discovered earlier. We complete the task by…
In this paper, we develop a Cauchy matrix reduction technique that enables us to obtain solutions for the reduced local and nonlocal complex equations from the Cauchy matrix solutions of the original before-reduction systems. Specifically,…
Multiple-try Metropolis (MTM) is a popular Markov chain Monte Carlo method with the appealing feature of being amenable to parallel computing. At each iteration, it samples several candidates for the next state of the Markov chain and…
This article introduces a new fast direct solver for linear systems arising out of wide range of applications, integral equations, multivariate statistics, radial basis interpolation, etc., to name a few. \emph{The highlight of this new…
We establish center manifold theorems that allow one to study the bifurcation of small solutions from a trivial state in systems of functional equations posed on the real line. The class of equations includes most importantly nonlinear…
Nonlocal models and their associated theories have been extensively investigated in recent years. Among these, nonlocal versions of the classical Laplace operator have attracted the most attention, while higher-order nonlocal operators have…
We present exact solutions describing dynamics of two algebraic solitons in the massive Thirring model. Each algebraic soliton corresponds to a simple embedded eigenvalue in the Kaup--Newell spectral problem and attains the maximal mass…
We show the existence of solution for some classes of nonlocal problems. Our proof combines the presence of sub and supersolution with the pseudomonotone operators theory.
The forced soliton equation is the starting point for semiclassical computations with solitons away from the small momentum transfer regime. This paper develops necessary analytical and numerical tools for analyzing solutions to the forced…
Weakly nonlocal thermodynamic theories are critically revisited. A relocalized, irreversible thermodynamic theory of nonlocal phenomena is given, based on a modified form of the entropy current and new kind of internal variables, the so…
General $N$-solitons in three recently-proposed nonlocal nonlinear Schr\"odinger equations are presented. These nonlocal equations include the reverse-space, reverse-time, and reverse-space-time nonlinear Schr\"odinger equations, which are…
In this paper, we investigate a general integrable nonlocal coupled nonlinear schr\"odinger (NLS) system with the the parity-time (PT) symmetry, which contains not only the nonlocal self-phase modulation and the nonlocal cross-phase…