On Discretizations of the Vector Nonlinear Schrodinger Equation

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.

16 pages, 1 figure, 1 table

References in corpus (2)

• Inelastic Collision and Switching of Coupled Bright Solitons in Optical Fibers
• Temperature Correlation of Quantum Spins

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