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Inverse scattering transform for the integrable nonlocal nonlinear Schrödinger equation

Inverse scattering transform for the integrable nonlocal nonlinear Schrödinger equation

Ziad H. Musslimani (Florida State University)
Veranstaltungsdatum: 22. Juni 2016 14:00 Uhr
 Raum 4.331 (NWZ II)

Inverse scattering transform for the integrable nonlocal nonlinear Schrödinger equation

Im Seminar des Instituts für Analysis, Dynamik und Modellierung spricht am Mittwoch, den 22. Juni 2016 um 14.00 Uhr Ziad H. Musslimani (Florida State University).

A nonlocal nonlinear Schrödinger (NLS) equation was recently introduced in Phys. Rev. Lett. 110, 064105 (2013) and shown to be an integrable infinite dimensional Hamiltonian evolution equation. In this talk we present a detailed study of the inverse scattering transform of this nonlocal NLS equation. The direct and inverse scattering problems are analyzed. Key symmetries of the eigenfunctions and scattering data and conserved quantities are discussed. The inverse scattering theory is developed by using a novel left-right Riemann-Hilbert problem. The Cauchy problem for the nonlocal NLS equation is formulated and methods to find pure soliton solutions are presented; this leads to explicit time-periodic one and two soliton solutions. A detailed comparison with the classical NLS equation is given and brief remarks about nonlocal versions of the modified Korteweg-de Vries and sine-Gordon equations are made.