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by; A. N. Njah, Department of Physics, University of Agriculture, Abeokuta, Nigeria.
and R. Akin-Ojo, Department of Physics, University of Ibadan, Ibadan, Nigeria
Abstract
The Non-linear Schrodinger Equation (NLSE), (in units of where is a positive real constant, and is a real constant, E is the energy, is known to be integral for infinite X space. A Fourier analysis in a bounded interval , i.e. shows that the NLSE is a nonlinear Hamiltonian system of N degrees of freedom. The effect of truncating the degrees of freedom to a finite number N and the fact that L is finite are investigated for the case and . The results show that chaos sets in at certain value of the energy as the energy – increases for fixed N. Hence the NLSE is not integrable for finite N, and L. However, the integrability increases with increase in N implying that as N tends to infinity the NLSE becomes completely integrable as expected.
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