Determining the fundamental conditions of the soliton solution for the new nonlocal discrete

Abstract

The purpose of this research is to present a new model for the nonlocal reductions of the multi-component discrete Manakov system. In particular, the focusing solution is determined based on a special condition of the potential function. This study includes: solving the spectral problem and finding the eigenfunctions and the scattering data. The importance of our study lies in examining the conditions distinguishing the solution called a soliton. There are two cases of the potential functions: single and double excitations, if the Lax operator has no spectrum neither outside nor inside the unit circle then, there is no soliton solution, this happens with a single site case. On the other hand, the two-site case gives two soliton solutions. It is shown that the soliton is more likely to occur at the discrete eigenvalues outside or inside the unit circle, as the excitations are more than one. Each case introduced is supported by numerical simulations.

Keywords

• nonlocal nonlinear schro ̈dinger equation,,
• ,،soliton solutions,,
• ,،manakov model