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The cubic nonlinear Schr\"odinger equation and some of its discretizations, one of which is integ- rable, are studied. Apart from the integrable version the discretizations produce chaotic solutions for intermediate levels of mesh (mode) refinement. Chaos disappears when the discretization is fine enough and convergence to a quasiperiodic solution is obtained. Details are given for finite difference calculations, although similar results are also obtained by Fourier spectral methods. Results regarding a forced nonlinear Schr\"odinger equation are briefly described.
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Herbst et al. (1989) studied this question.
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