The semiclassical limit of the defocusing nonlinear Schroedinger flows.
AdvisorLevermore, C. David
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PublisherThe University of Arizona.
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AbstractThe Lax-Levermore strategy for analyzing the zero-dispersion limit of the KdV equation through its inverse scattering transform can be adapted to study the semiclassical limits of the defocusing nonlinear Schrodinger (NLS) equation, which are in fact the limits of corresponding conservation laws. The weak limits of all conserved densities and their fluxes can be characterized in terms of the solution of a variational problem that in turn can be solved using function theory. These results rest on a new formula for the N-soliton solutions and a WKB analysis of the semiclassical limit for the direct and inverse Zakharov-Shabat scattering transform. Moreover, with Levermore's method, one can see that the limiting dynamics explored is hyperbolic and agrees with that obtained by classical nonlinear modulation theory. The result is extended to the whole NLS hierarchy.
Degree ProgramApplied Mathematics