Homework SourseUx t 2k2sech2kx 4k3t delta 2k2 1 tanh2kx 4k3 t delta
U(x, t) = 2k^2sech^2(kx - 4k^3t + delta) = 2k^2 [1 - tanh^2(kx - 4k^3 t + delta)]. Make a graph of the hump-type wave (5) at t = 0 for k = 2, and delta = 0. Show graphically that as time increases (take different values for t), the solitary wave with amplitude 2k^2 = 8 travels to the right at phase velocity u = omega/k = 4k^2 = 16. Note that the phase velocity is exactly twice the peak amplitude.![U(x, t) = 2k^2sech^2(kx - 4k^3t + delta) = 2k^2 [1 - tanh^2(kx - 4k^3 t + delta)]. Make a graph of the hump-type wave (5) at t = 0 for k = 2, and delta = 0. Sh](/WebImages/32/ux-t-2k2sech2kx-4k3t-delta-2k2-1-tanh2kx-4k3-t-delta-1093290-1761576020-0.webp "U(x, t) = 2k^2sech^2(kx - 4k^3t + delta) = 2k^2 [1 - tanh^2(kx - 4k^3 t + delta)]. Make a graph of the hump-type wave (5) at t = 0 for k = 2, and delta = 0. Sh")
Solution
