Robust inverse scattering transform in a Kundu-nonlinear Schrödinger equation under non-zero and zero backgrounds: breathers, rogue waves and higher-order solitons

Abstract In the work, we study the robust inverse scattering transform in a Kundu-nonlinear Schrödinger equation under non-zero and zero backgrounds. For non-zero backgrounds, we construct the Riemann-Hilbert problem and develop the corresponding N -fold Darboux transform, from which the breathers and rogue waves get derived. By means of asymptotic analysis and graphical simulation, dynamics of the second-order spatial period and temporal period breathers is presented. Through numerical simulations, we demonstrate the stability of these solutions under both noise-free and perturbed conditions. For zero backgrounds, higher-order soliton solutions get obtained. Subsequent asymptotic analysis yields asymptotic soliton solutions which are found to closely approximate the exact soliton solutions. The results of this work can provide theoretical references for understanding localized wave dynamics in nonlinear physical systems.