We consider the radial differential operator for a fixed angular mode \(n\), \[ L_n=\frac{d^2}{d r^2}+\frac{1}{r} \frac{d}{d r}-\frac{n^2}{r^2}, \quad r \in(0, \infty) \]

Claim: \[ \mathscr{H}_{m+1}\left[\left(\partial_r-\frac{m}{r}\right) f_m\right]=-k \hat{f}_m \]

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basic concept ninja ninja is a build system—a tool that actually runs the compile and link commands for a software project. T...

The case in which the water has infinite depth is considered, the effect of surface tension as well.

This is the notes for Chapter 5.4, mainly about ship waves.