arXiv subjects
Publications and source records attributed to A. D. Trubatch.
The scalar nonlinear Schrodinger (NLS) equation and a suitable discretization are well known integrable systems which exhibit the phenomena of ``effective'' chaos. Vector generalizations of both the continuous and discrete system are discussed. Some attention is directed upon the issue of the integrability of a discrete version of the vector NLS equation.
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.