Generalized $T\overline{T}$-like Deformations in Duality-Invariant Nonlinear Electrodynamic Theories

This study introduces a high-order perturbation methodology to categorize two primary solution types within duality-invariant nonlinear electrodynamic theories, adhering to the differential self-duality criterion. The first solution type aligns with irrelevant stress tensor flows, resembling $T\bar{T}$ dynamics, and the second involves a blend of irrelevant $T\bar{T}$-like and marginal root-$T\bar{T}$-like deformations. Our approach facilitates the investigation of diverse duality-invariant nonlinear electrodynamics theories and their stress tensor flows and confirms the commutativity of flows initiated by irrelevant and marginal operators.