Rational vector rogue waves for the n-component Hirota equation with non-zero backgrounds

Abstract In this paper, the dimensionless n -component Hirota (alias the n -Hirota) equation is investigated, which describes the wave propagations of n ultrashort optical fields in a fiber. Starting from the modified Darboux transform and its Lax pair with initial non-zero plane-wave conditions, we find the novel multi-parametric families of rational vector rogue wave (RW) solutions for the n -Hirota equation. Furthermore, some weak and strong interactions of rational vector RWs are exhibited for the n -Hirota equation with n = 2 , 3 , 4 , 5 , 6 in detail. In particular, we also deduce the rational vector W -shaped dark and bright solitons of the n -component complex mKdV equation, whose representative wave structures are illustrated for n = 2 , 3 , 4 , 5 . Finally, the effect of a small non-integrable deformation of the 3-Hirota equation is explored numerically on the excitation of vector RWs in terms of the Fourier spectral method. These obtained rational vector RW and W-shaped soliton solutions will be useful to further explore the related nonlinear wave phenomena in the sense of multi-component physical systems with non-zero backgrounds.