Lecture 23, 18.376, Thu May 4, 2023.
Summary
From the "Lecture Topics" notes posted on the web page.
  Finish  "3.3 Turning points: transitions from waves to no-wave"
  Cover   "4.1.3 The Fourier Transform approach."

4.1.3 show that, when the equation k_t + c_g(k)_x = 0 develops multiple
values, the resolution is NOT to introduce shocks, but actually use the
multiple values. The modulation solution is then valid everywhere,
except near the caustics [envelope of the characteristics for
k_t + c_g(k)_x = 0], where (typically) an Airy function characterizes
the transition from "waves to no waves" as pairs of waves cancel out
along a caustic.
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