On Discretizations of the Vector Nonlinear Schrodinger Equation

Details On Discretizations of the Vector Nonlinear Schrodinger Equation On Discretizations of the Vector Nonlinear Schrodinger Equation

1998-10-19

arxiv.org/abs/solv-int/9810014v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

16 pages, 1 figure, 1 table

Scientific paper

10.1016/S0375-9601(99)00048-1

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.

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