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The nonlinear cubic Shrödinger equation is integrated numerically for quantum
systems confined by potential walls of a well. If nonlinear potential describing nonlinearity is
distributed on the whole width of the well, soliton generation is possible. For the nonlinear
potential distributed on the right half of the well with free motion on the left one the
propagation of waves occurs. Solutions for the probability density, expectation positions and
velocities of the wave were analyzed under different initial conditions including the Gaussian
and specified wave packets.
Keywords: the nonlinear cubic Shrödinger equation; soliton |
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