A Proof of the Soliton Resolution Conjecture for the Focusing Nonlinear Schrödinger Equation
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PublisherThe University of Arizona.
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AbstractWe give a proof of the long-time asymptotic behavior of the focusing nonlinear Schrödinger equation for generic initial condition in which we have simple discrete spectral data and an absence of spectral singularities. The proof relies upon the theory of Riemann-Hilbert problems and the ∂ ̄ method for nonlinear steepest descent. To leading order, the solution will appear as a multi-soliton solution as t → ∞.
Degree ProgramGraduate College