Inverse scattering transform for the time dependent Schrödinger equation with applications to the KPI equation
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For the direct-inverse scattering transform of the time dependent Schrödinger equation, rigorous results are obtained based on an opertor-triangular-factorization approach. By viewing the equation as a first order operator equation, similar results as for the first ordern x n matrix system are obtained. The nonlocal Riemann-Hilbert problem for inverse scattering is shown to have solution.
KeywordsNeural Network Statistical Physic Complex System Nonlinear Dynamics Quantum Computing
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