2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/159559Addition of higher nonlinear terms to the well known integrable nonlinear Schrödinger (NLS) equations, keeping the same linear dispersion (LD) usually makes the system nonintegrable. We present a systematic method through a novel Eckhaus-Kundu hierarchy, which can generate higher nonlinearities in the NLS and derivative NLS equations preserving their integrability. Moreover, similar nonlinear integrable extensions can be made again in a hierarchical way for each of the equations in the known integrable NLS and derivative NLS hierarchies with higher order LD, without changing their LD.Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/Exactly Solvable and Integrable SystemsStatistical MechanicsHigh Energy Physics - TheoryMathematical Physicstext