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Analysis of the broadband gain of a GaInNAs single quantum well (QW) semiconductor optical amplifier (SOA) is developed considering the tuneability of the gain in detail. The SOA is analyzed as a single device multiwavelength channel amplifier in a wavelength-division-multiplexing (WDM) network. The gain model includes the QW material gain derived using a band anti-crossing model and includes quantum dot (QD) fluctuations in the conduction band arising from compositional fluctuations of N within the QW. The material gain is broadened by adding the gain of the QD-like fluctuations and the QW confined level. Simultaneous amplification of two optical signals is analyzed, one at the peak of the QW gain and one at the peak of the QD distribution gain, and the linear and nonlinear regions are established. In addition, multi-channel signal amplification, appropriate for WDM applications, has been modeled across the frequency range of the QW and the QD-like fluctuations and no wavelength degradation between the channels was observed demonstrating the potential of dilute nitride QW as multiwavelength SOAs at optical communications wavelengths.