Inverse scattering transforms of the inhomogeneous fifth-order
defocusing nonlinear Schrodinger equation with zero boundary conditions
and nonzero boundary conditions: bound-state solitons and rogue waves
Abstract
The present work studies the inverse scattering transformation (IST) of
the inhomogeneous fifth-order defocusing nonlinear Schrodinger (ifoNLS)
equation with zero boundary conditions (ZBCs) and non-zero boundary
conditions (NZBCs). Firstly, the bound-state (BS) solitons of the ifoNLS
equation with ZBCs are derived by generalization of the residue theorem
and the Laurent’s series for the first time. Then combining with the
robust IST, the matrix Riemann-Hilbert (RH) problem of the ifoNLS
equation with NZBCs are revealed. Based on the resulting RH problem, a
new higher-order rogue wave (RW) solution of the ifoNLS equation are
found by the modified Darboux transformation. Finally, some
corresponding graphs are given by selecting appropriate parameters to
further discuss the unreported dynamic behavior of the BS solitons and
RW solutions, which have not been reported before.