Sine-Gordon equation

The Sine-Gordon equation is a partial differential equation for a function φ of two real variables, x and t, given as follows:

${\frac {d^{2}\phi }{dt^{2}}}-{\frac {d^{2}\phi }{dx^{2}}}+\sin \phi =0$.

This PDE describes solitons.

See also Bäcklund transform.