Question

Consider the linear KdV with advection,

∂tu = −∂^3 xu + c∂xu, u(x, 0) = u0(x).

Find the phase and group velocities

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Answer 1

Answer:

∂tu = c∂xu, u(x, 0) = u0(x) with x ∈ R and t ∈ R is given by u(x, t) = u0(x + ct),. i.e. the initial function u0 is shifted with a velocity c to the left