The method of multiple scales is used to derive a new integrable coupled nonlinear Schr\\"odinger equation (CNLS) as an amplitude equation from the coupled nonlinear Klein-Gordon Equation (CNKG). We also give the corresponding spectral problem and further reduce the derived equation into a finite dimensional integrable Hamiltonian system. Finally the integrability of the reduced system is deduced by using a perturbation analysis.
ÖZER, MEHMET NACİ (1998) "A New Integrable Reduction of the Coupled NLS Equation," Turkish Journal of Mathematics: Vol. 22: No. 3, Article 6. Available at: https://journals.tubitak.gov.tr/math/vol22/iss3/6