Asymptotic stability of plane wave solutions for the Schrödinger–Langevin–Kostin equation

This paper studies the stability of plane wave solutions for the one-dimensional Schrödinger–Langevin–Kostin equation. By explicitly computing the eigenvalues of the linearized operator for the reduced system under a simplifying assumption that eliminates the complicated dissipative term, we establish the asymptotic stability of plane wave solutions in Sobolev spaces. Our theoretical result agrees with prior numerical studies on the Schrödinger–Langevin–Kostin equation.