Generalized perturbation (n, N − n) fold Darboux transformation for a nonlocal Hirota equation with variable coefficients

Abstract

Abstract In this paper, a nonlocal Hirota equation with variable coefficients is investigated by applying the generalized perturbation (n, N − n) fold Darboux transformation method and Taylor expansion method. Multi-soliton solutions are obtained when the seed solution is trivial, and multi-soliton solutions, multi-breather solutions, high-order rogue wave solutions and their interaction solutions are obtained when the seed solution is a plane wave solution. Especially, we get the interaction solution of soliton, breather and rogue wave solution. In addition, by choosing appropriate parameters, the dynamic behaviors of the obtained solution are explored.