Superconducting traveling-wave parametric amplifiers are a promising amplification technology suitable for applications in submillimeter astronomy. Their implementation relies on the use of Floquet transmission lines in order to create strong stopbands to suppress undesired harmonics. For design, amplitude equations are used to predict their gain. However, they do not take into account the complex dispersion and impedance that result from the use of Floquet lines, hindering reliable design. In order to overcome this limitation, we have used the multiple-scales method to include those effects. We demonstrate that complex dispersion and impedance have a stark effect on the gain, even suppressing it completely in certain cases. The equations presented here can, thus, guide to a better design and understanding of the properties of this kind of amplifiers.