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

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