When you start looking at #NonlinearWaves, some of these principles no longer apply. For example, in the Korteweg-de Vries equation, which has #Soliton or solutions, you can no longer simply add two solutions together as the resulting function would not be a solution of the governing equation. Waves of different heights travel at different velocities, with the taller waves moving faster than the shorter ones. Instead, they interact #nonlinearly.

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#Mathematics #AppliedMathematics #Physics