Nowadays, improving the accuracy of computational methods to solve the initial value
problem of the Zakharov-Shabat system remains an urgent problem in optics. In particular …

We propose a finite-difference algorithm for solving the initial problem for the Zakharov-
Shabat system. This method has the fourth order of accuracy and represents a …

The direct Zakharov–Shabat scattering problem has recently gained significant attention in
various applications of fiber optics. The development of accurate and fast algorithms with …

The nonlinear Schrödinger equation (NLSE) is widely used in telecommunication
applications, since it allows one to describe the propagation of pulses in an optical fiber …

We propose a novel algorithm for the numerical computation of discrete eigenvalues in the
Zakharov–Shabat problem. Our approach is based on contour integrals of the nonlinear …

We present two numerical methods for the approximation of the generalized Zakharov
system (ZS). The first one is the time-splitting spectral (TSSP) method, which is explicit, time …

The generalized Zakharov system (ZS) couples a dispersive field E (scalar or vectorial) and
J nondispersive fields {n_j\} _ j= 1^ J with a propagating speed of 1/\in_j. In this paper, we …

A new conservative difference scheme is presented for the periodic initial-value problem of
Zakharov equations. The scheme can be implicit or semi-explicit, depending on the choice …

In this paper, we propose and study two time-splitting spectral methods for the generalized
Zakharov system. These methods are spectrally accurate in space, second order in time …

We present two uniformly accurate numerical methods for discretizing the Zakharov system
(ZS) with a dimensionless parameter 0<ε\le1, which is inversely proportional to the acoustic …