Spectral structure and even-order soliton solutions of a defocusing shifted nonlocal NLS equation via Riemann-Hilbert approach

Utilizing the Riemann-Hilbert (RH) approach, we shed light on the spectral structure of a defocusing shifted nonlocal NLS equation with a space-shifted parameter from which we derive its soliton solutions. The spectral structure involves the scattering data and their corresponding symmetry relations. Firstly, by performing spectral analysis of the corresponding Lax pair, we explore in detail the spectral structure of the defocusing shifted nonlocal NLS equation. It is shown that the zeros of the RH problem of the defocusing shifted nonlocal NLS equation do not allow for purely imaginary ones, which is rather different from its focusing counterpart. Secondly, based on the revealed spectral structure, the even-order soliton solutions of the defocusing shifted nonlocal NLS equation are rigorously obtained. Thirdly, the dynamical properties underlying the obtained soliton solutions are analyzed and then graphically illustrated by highlighting the role that the space-shifted parameter plays.