Tsunami - Mathematical classification
Short answer: Tsunami models use the shallow-wave mathematical approach, because their wavelength is usually much larger than the relevant water depth determining their propagation.

Long answer:
Tsunamis are often called 'tidal waves' to highlight the idea that their characteristic time response is closer to tydes than to the standard wind waves we are used to see in a beach. The full spectrum of water wave periods is shown in this figure (tsunamis being classified as long-period waves, together with waves caused by meteorological events):
Classification of the spectrum of ocean waves according to wave period. Redrawn from Figure 1 in: Walter H. Munk (1950) "Origin and generation of waves". Proceedings 1st International Conference on Coastal Engineering, Long Beach, California. ASCE, pp. 1–4.

This image shows that the wave frequency depends on the cause behind the perturbation of the water surface. 

Oceanographers generally treat ocean waves as free surface waves in an ideal fluid [2]. 

Mathematically, tsunamis are surface gravity waves approached as shallow-water waves (see chapter 4.1.5 in here), meaning that the wavelength λ > 20H (H being the water depth). The involved shallow-water-wave mathematical approximations oppose to the deep-water waves (λ &lt; H, see section 4.1.4 in the same [ref 3]). 

Whereas for shallow waves the wave frequency and the wave speed are (ref. 3):

$ω = \sqrt {g k 2H}$    with $k = 2\pi / \lambda$

$c = \sqrt {g H}$

for deep-water waves, instead:  

$ω = \sqrt {g k}$ 

$c = \sqrt {\frac{g \lambda}{2\pi}}$

As the wave approaches the shore and H decreases, the wave velocity decreases and energy is preserved by increasing the wave amplitude.  

Detailed information here: 3.