A tsunami is mathematically modeled by a particular form of a partial differential equation (PDE). Do a search for "soliton", "PDE", "mathematical", and/or "model" and I bet you'll find tons of web pages on the subject.
PDEs are often introduced to juniors/seniors in college who have had three semesters of calculus and one semester of ordinary differential equations. And even then, typically you aren't taught how to solve any but the most basic PDEs. Thus, to understand it, you need knowledge that is well beyond algebra. A true PDE class is typically first taught to masters students in math and engineering. There will be several other more advanced PDE courses for advanced masters and PhD students in math and engineering.
A typical PDE for a soliton may look like this (from a googled web page):
(du/dt) + 6 * u * (du/dx) + (d^3u/dx^3) = 0
where u is the height of the water, t is time, x is position. One particular solution to that equation looks like this:
u = sech[ a^0.5 * (x - 2 * t * a) / 2^0.5 ]^2 * a
where a is a constant (varies with the magnitude of the original disturbance). Of course, this is just a 2-D model of a soliton travelling in one direction (probably a decent simplification). The Earth is curved and that would really complicate matters beyond ability to get an algebraic solution. Or we can include other real world problems (such as uneven ocean floor height when the soliton approaches land). Something like that would really make algebraic solution impossible.