A discrete analog of a skew selfadjoint canonical (Zakharov-Shabat or AKNS) system with a pseudo-exponential potential is introduced. For the corresponding Weyl function the direct and inverse problem are solved explicitly in terms of three parameter matrices. As an application explicit solutions are obtained for the discrete integrable nonlinear equation corresponding to the isotropic Heisenbe...

Introduction: Inverse scattering transform holds a central place in the analysis of nonlinear integrable system in either (1+1)or (2+1)-dimensions [1]. On the other hand it has been found that explicit soliton solutions can also be obtained by the use of Bäcklund transformations in a much easier way [2]. These Bäcklund transformations are also useful in proving the superposition formulae for th...

In this talk, we present efficient and stable numerical methods for the generalized Zakharov system (GZS) describing the propagation of Langmuir waves in plasma. The key point in designing the methods is based on a time-splitting discretization of a Schroedinger-type equation in GZS, and to discretize a nonlinear wave-type equation by pseudospectral method for spatial derivatives, and then solv...

Abstract We derive the $$2\hbox {d}$$ 2d Zakharov–Mikhailov action from $$4\hbox xmlns:mml="http://www.w3.org/1998/Math/MathML">4d Chern–Simons theory. This is known to produce as equations of mot...

Abstract A degenerate Zakharov system arises as a model for the description of laser-plasma interactions. It is coupled Schrödinger and wave equation with non-dispersive direction. In this paper, new local well-posedness result rough initial data established. The proof based on an efficient use smoothing maximal function norms.