Essentially nonlinear one-dimensional model of classical field theory

It is shown that the equation $u_{tt}-u_{xx}+\sin u=0$ with boundary condition $u(x,t)\to 0$ $(\operatorname{mod}2\pi)$ as $|x|\to\infty$, which describes a classical field with essentially nonlinear interaction, is a completely integrable Hamiltonian system. The results are interpreted in terms of particles corresponding to the field $u(x,t)$.