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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 Nonlinear Schrdinger Equation (NLSE) in units of
where are real parameters, p is a positive integer and is the eigenvalue (energy) is solved by numerical and perturbation methods in an infinite potential well vis-a-vis the linear Schrodinger (LSE). The eigenvalue for the n eigenvalue in the well is found for the cases p = 2[4] to be given by where a = 2.46831[2.46773], b = -0.065982[-0.039568] and c = 1[1] using the numerical method. Using the perturbation method leads to similar results. These results are comparable with those of the LSE: , where k = 2.5. have the effect of increasing the values of the Also as p increases for the NLSE tends to for the LSE. The analysis confirms that the NLSE describes small amplitude waves, which are also self energizing.
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