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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- [B-C]. Beals, R., Coifman, R. R.: Scattering and inverse scattering for first order systems. Commun. Pure Appl. Math.37, 39–90 (1984)Google Scholar
- [D-T]. Deift, P., Trubowitz, E.: Inverse scattering on the line. Commun. Pure Appl. Math.32, 121–251 (1979)Google Scholar
- [F-A]. Fokas, A. S.: On the inverse scattering of the time-dependent Schrödinger equation and the associated Kadomtsev-Petviashvili (I) equation. Stud. Appl. Math.69, 211–228 (1983)Google Scholar
- [M]. Manakov, S. V.: Physica3D, 420 (1981)Google Scholar
- [S]. Segur, H.: Comments on IS for the Kadomtsev-Petviashvili equation, in: Mathematical methods in hydrodynamics and integrability in dynamical systems. AIP Conference Proceedings88, 211–228 (1982)Google Scholar
- [Z-M]. Zakharov, V. E.: Manakov, S. V.: Sov. Sci. Rev. Phys. Rev.1, 133 (1979)Google Scholar
- [Z]. Zhou, X.: Direct and inverse scattering transforms with arbitrary spectral singularities. Commun. Pure. Appl. Math.42, 895–938 (1989)Google Scholar