In this paper the method of multiple scales is used to derive an integrable matrix non-linear Schrödinger equation (MNLS) as an amplitude equation from the Matrix Korteweg-de Vries equation (MKdV) associated with symmetric spaces. Then the integrability of the MNLS equation is deduced by the derivation of the spectral problem for the MNLS equation from the spectral problem for the MKdV equation.
ÖZER, Mehmet Naci (1998) "Multiple Scales Method for a Matrix KdV Equation," Turkish Journal of Physics: Vol. 22: No. 9, Article 7. Available at: https://journals.tubitak.gov.tr/physics/vol22/iss9/7