Orbital Stability of Soliton for the Derivative Nonlinear Schrödinger Equation in the $L^2$ Space

In this paper, we establish the orbital stability of the 1-soliton solution for the derivative nonlinear Schrödinger equation under perturbations in $L^2(\mathbb{R})$. We demonstrate this stability by utilizing the Bäcklund transformation associated with the Lax pair and by applying the first conservation quantity in $L^2(\mathbb{R})\mathrm{.}$