On Discretizations of the Vector Nonlinear Schrodinger Equation

1998/10/19 by M. J. Ablowitz, Y. Ohta, A. D. Trubatch · 2 citations
Physics and Astronomy · #solv-int #nlin.SI

paper · pdf · doi:10.1016/s0375-9601(99)00048-1

16 pages, 1 figure, 1 table

arxiv created 1998/10/19 · arxiv updated 2009/11/30

Abstract

Two discretizations of the vector nonlinear Schrodinger (NLS) equation are studied. One of these discretizations, referred to as the symmetric system, is a natural vector extension of the scalar integrable discrete NLS equation. The other discretization, referred to as the asymmetric system, has an associated linear scattering pair. General formulae for soliton solutions of the asymmetric system are presented. Formulae for a constrained class of solutions of the symmetric system may be obtained. Numerical studies support the hypothesis that the symmetric system has general soliton solutions.

Cited by

• Novel periodic solutions and rogue waves of the defocusing scalar and coupled Ablowitz-Ladik systems on a nonzero background
• Soliton and breather interactions in the integrable discrete focusing Manakov system via Hirota's method