The higher-order nonlinear Schrodinger equation with non-zero boundary conditions: Robust inverse scattering transform, breathers, and rogons

An integrable three-parameter fifth-order nonlinear Schrodinger equation with non-zero boundary conditions was studied staring from its Lax pair and a robust inverse scattering transform such that one-, and n-fold modified Darboux transforms (DTs) are presented. For distinct parameters, the one-fold DT is used to simultaneously investigate its first- and second-order breathers, rational W-shaped soliton-like solutions, and rogons. Moreover, we also analyze their wave structures, and relations between these solutions and special parameters. The n-fold DT is also established for the fifth-order NLS equation such that its (2n -1, 2n)th-order rogue wave solutions can be found simultaneously. Particularly, we exhibit the third- and fourth-order rogon structures. All these results can also reduce to ones for the special cases of the fifth-order NIS equation such as the NLS equation, Hirota equation, and Lakshmanan-Porsezian-Daniel equation. (C) 2019 Elsevier B.V. All rights reserved.