Related papers: Integrable Nonlocal Reductions
We study the nonlocal modified Korteweg-de Vries (mKdV) equations obtained from AKNS scheme by Ablowitz-Musslimani type nonlocal reductions. We first find soliton solutions of the coupled mKdV system by using the Hirota direct method. Then…
We present nonlocal integrable reductions of super AKNS coupled equations. By the use of nonlocal reductions of Ablowitz and Musslimani we find new super integrable equations. In particular we introduce nonlocal super NLS equations and the…
In this paper, we provide several novel solutions of the Ablowitz-Musslimani as well Yang's versions of the nonlocal nonlinear Schr\"odinger (NLS) equation, nonlocal modified Korteweg-de Vries (mKdV) as well as nonlocal Hirota equations. In…
We provide several novel solutions of the coupled Ablowitz-Musslimani (AM) version of the nonlocal nonlinear Schr\"odinger (NLS) equation and the coupled nonlocal modified Korteweg-de Vries (mKdV) equations. In each case we compare and…
We study standard and nonlocal nonlinear Schr\"{o}dinger (NLS) equations obtained from the coupled NLS system of equations (Ablowitz-Kaup-Newell-Segur (AKNS) equations) by using standard and nonlocal reductions respectively. By using the…
In the paper possible local and nonlocal reductions of the Ablowitz-Kaup-Newell-Suger (AKNS) hierarchy are collected, including the Korteweg-de Vries (KdV) hierarchy, modified KdV hierarchy and their nonlocal versions, nonlinear…
We obtain novel periodic as well as hyperbolic solutions of an Ablowitz-Musslimani variant of the coupled nonlocal, nonlinear Schr\"odinger equation (NLS) as well as a coupled nonlocal modified Korteweg-de Vries (mKdV) equation which can be…
We show that a number of nonlocal nonlinear equations including the Ablowitz-Musslimani and the Yang variant of the nonlocal nonlinear Schr\"od-inger (NLS) equation, nonlocal modified Korteweg de Vries (mKdV) equation as well as the…
It is well known that the nonlinear Schr\"odinger (NLS) equation is a very important integrable equation. Ablowitz and Musslimani introduced and investigated an integrable nonlocal NLS equation through inverse scattering transform. Very…
The method of nonlinearization of the Lax pair is developed for the Ablowitz-Kaup-Newell-Segur (AKNS) equation in the presence of space-inverse reductions. As a result, we obtain a new type of finite-dimensional Hamiltonian systems: they…
We present nonlocal integrable reductions of the Fordy-Kulish system of nonlinear Schrodinger equations and the Fordy system of derivative nonlinear Schrodinger equations on Hermitian symmetric spaces. Examples are given on the symmetric…
Starting from a multi-component AKNS system, we obtain new shifted nonlocal nonlinear Schr\"{o}dinger equations. We find 13 different shifted nonlocal nonlinear Schr\"{o}dinger equations with two-place nonlocalities and 10 shifted nonlocal…
A nonlocal nonlinear Schr\"odinger (NLS) equation was recently found by the authors and shown to be an integrable infinite dimensional Hamiltonian equation. Unlike the classical (local) case, here the nonlinearly induced "potential" is $PT$…
We first study coupled Hirota-Iwao modified KdV (HI-mKdV) systems and give all possible local and nonlocal reductions of these systems. We then present Hirota bilinear forms of these systems and give one-soliton solutions of them with the…
We investigate the complete integrability of soliton equations with shifted nonlocal reductions under the rapidly decreasing boundary conditions. The illustrative examples we choose are the Ablowitz-Ladik (AL) system and the…
Integrable and nonintegrable discrete nonlinear Schr\"odinger equations (NLS) are significant models to describe many phenomena in physics. Recently, Ablowitz and Musslimani introduced a class of reverse space, reverse time and reverse…
We study the local and shifted nonlocal reductions of the integrable coupled Kundu type system. We then consider particular cases of this system; namely Chen-Lee-Liu, Gerdjikov-Ivanov, and Kaup-Newell systems. We obtain one- and two-soliton…
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…
Quasi-monochromatic complex reductions of a number of physically important equations are obtained. Starting from the cubic nonlinear Klein-Gordon (NLKG), the Korteweg-deVries (KdV) and water wave equations, it is shown that the leading…
Writing the Hirota-Satsuma (HS) system of equations in a symmetrical form we find its local and new nonlocal reductions. It turns out that all reductions of the HS system are Korteweg-de Vries (KdV), complex KdV, and new nonlocal KdV…