Semi-rational vector rogon–soliton solutions and asymptotic analysis for any n-component nonlinear Schrödinger equation with mixed boundary conditions

In this paper, we investigate the wave structures of any n-component nonlinear Schrödinger (alias n-NLS) equation with mixed nonzero and zero boundary conditions, which can be used to describe the interactions of many bodies in differential fields. As a consequence, we find its semi-rational vector rogon–soliton solutions (non-zero backgrounds) and soliton-like solutions (zero backgrounds) with the aid of the modified Darboux transform and the multiple root of an (n+1)th degree characteristic polynomial equation. Moreover, the semi-rational vector rogon–soliton solutions can be shown to be PT-symmetric for chosen parameters, and decomposed into rational rogons and grey-like solitons for the bigger parameters. Finally, the maximum amplitudes and average amplitudes are analysed for the semi-rational vector rogon–soliton solutions for some choice of parameters. These results will be useful to better understand the relative physical phenomena in the n-NLS equation or other related multi-component nonlinear physical models. •Novel semi-rational vector rogon–soliton solutions are obtained.•Strong and weak interactions of semi-rational vector solutions are studied.•Asymptotic analysis of semi-rational vector solutions is investigated.•Maximum amplitudes and average amplitudes are analysed for the semi-rational solutions.