# Modulation parameters

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When a solution is close to a soliton at each time *t*, the position, amplitude, phase, etc. of the soliton that best approximates the solution are collectively known as the **modulation parameters**. One has some freedom regarding how to define the "best" approximation, but once one does, these parameters will obey some ordinary differential equations (coupled with a PDE governing the error term between the solution and the soliton), known as the **modulation equations**.

The presence of modulation parameters is closely tied to the symmetries of the underlying equation.