Vector semi-rational rogon-solitons and asymptotic analysis for any multi-component Hirota equations with mixed backgrounds

The Hirota equation can be used to describe the wave propagation of an ultrashort optical field.In this paper,the multi-component Hirota(alias n-Hirota,i.e.n-component third-order nonlinear Schrodinger)equations with mixed non-zero and zero boundary conditions are explored.We employ the multiple roots of the characteristic polynomial related to the Lax pair and modified Darboux transform to find vector semi-rational rogon-soliton solutions(i.e.nonlinear combinations of rogon and soliton solutions).The semi-rational rogon-soliton features can be modulated by the polynomial degree.For the larger solution parameters,the first m(m<n)components with non-zero backgrounds can be decomposed into rational rogons and grey-like solitons,and the last n-m components with zero backgrounds can approach bright-like solitons.Moreover,we analyze the accelerations and curvatures of the quasi-characteristic curves,as well as the variations of accelerations with the distances to judge the interaction intensities between rogons and grey-like solitons.We also find the semi-rational rogon-soliton solutions with ultrahigh amplitudes.In particular,we can also deduce vector semi-rational solitons of the ncomponent complex mKdV equation.These results will be useful to further study the related nonlinear wave phenomena of multi-component physical models with mixed background,and even design the related physical experiments.