No - why should they?
What does happen is that in the open sea, a tsunami is felt as just a swell, as it has a very long wavelength, but small amplitude. As the wave approaches the coastline, the shallowing water causes the wave to "feel" the bottom and the wavelength effectively reduces but the height increases - sort of a concertina effect.
However (but!) there are frictional losses and interference from other waveforms, reflection, etc., so most tsunamis dissipate during their travel.
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