“The function ei(kx-ωt) represents a wave that travels at a speed of ω/k, which we have just shown to be equal to -k2. Therefore, the different plane-wave components of the solution travel at different speeds: the higher the angular frequency,… — Timothy Gowers Copy Share Image
“the simple algebraic equation ω+k3 = 0. This is called the dispersion relation of (1): with the help of the Fourier transform it is not hard to show that every solution is a superposition of solutions of the form ei(kx-ωt),… — Timothy Gowers Copy Share Image
