What can be said and done about the "SIGN-Gordon equation"?
$$\varphi\_{tt}- \varphi\_{xx} + \text{sgn}(\varphi) = 0.$$ 
It came up [here](https://mathoverflow.net/questions/22281/can-i-relate-the-l1-norm-of-a-function-to-its-fourier-expansion/).



Sign-Gordon Equation
Turns out it appears in literature as the "signum-Gordon equation". For example the paper 
[Signum-Gordon wave equation and its self-similar solutions](http://th-www.if.uj.edu.pl/acta/vol38/pdf/v38p3099.pdf)


