Pure soliton solutions of the nonlocal Kundu–nonlinear Schrödinger equation

Xiu-Bin Wang   ; Bo Han

Teoretičeskaâ i matematičeskaâ fizika, Tome 206 (2021) no. 1, pp. 47-78

Résumé

We systematically present an inverse scattering transform for a nonlocal reverse-space higher-order nonlinear Schrödinger equation with nonzero boundary conditions at infinity. We discuss two cases determined by two different values of the phase at infinity. In particular, for the direct problem, we study the analytic properties of the scattering data and the eigenfunctions and also find their symmetries. We study the inverse scattering problem obtained from the new nonlocal system using left and right Riemann–Hilbert problems with a suitable uniformization variable; we construct the time dependence of the scattering data. Finally, for these two phase values, we analyze the dynamics of solitons (solutions of the considered Schrödinger equation) in detail.

Détail

Keywords: nonlocal reverse-space higher-order nonlinear Schrödinger equation, inverse scattering transform, Riemann–Hilbert problem.

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