The method of multiple scales is used to derive separable nonlinear Schrödinger equations as amplitude equation from three component 2D nonlinear Klein-Gordon Equation. We further discuss the integrability of the derived separable amplitude equations and reduce them into finite dimensional Hamiltonian systems. Finally we give first integrals for the reduced systems.
ÖZER, MEHMET NACİ and ESER, DURSUN (1998) "Derivation of Separable Amplitude Equations by Multiple Scales Method," Turkish Journal of Mathematics: Vol. 22: No. 3, Article 5. Available at: https://journals.tubitak.gov.tr/math/vol22/iss3/5