Abstract
We report a numerical and theoretical study of the generation and propogation of oscillations in the semiclassical limit (h → 0) of the Nonlinear Schrödinger equation. In a general setting of both dimension and nonlinearity, we identify essential differences between the “defocusing” and “focusing” cases. Numerical comparisons of the oscillations are made between the linear (“free”) and the cubic (defocusing and focusing) cases in one dimension. The integrability of the one-dimensional cubic NLS is exploited to give a complete global characterization of the weak limits of the oscillations in the defocusing case.
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© 1994 Springer Science+Business Media New York
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Jin, S., Levermore, C.D., McLaughlin, D.W. (1994). The Behavior of Solutions of the NLS Equation in the Semiclassical Limit. In: Ercolani, N.M., Gabitov, I.R., Levermore, C.D., Serre, D. (eds) Singular Limits of Dispersive Waves. NATO ASI Series, vol 320. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-2474-8_18
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DOI: https://doi.org/10.1007/978-1-4615-2474-8_18
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