Breather

In physics, a breather is a nonlinear wave in which energy concentrates in a localized and oscillatory fashion.

This contradicts with the expectations derived from the corresponding linear system for infinitesimal amplitudes, which tends towards an even distribution of initially localized energy.

[1] But also the opposite situation: oscillations in space and localized in time[clarification needed], is denoted as a breather.

[4] Standing breathers correspond to localized solutions whose amplitude vary in time (they are sometimes called oscillons).

The sine-Gordon equation is the nonlinear dispersive partial differential equation with the field u a function of the spatial coordinate x and time t. An exact solution found by using the inverse scattering transform is:[1] which, for ω < 1, is periodic in time t and decays exponentially when moving away from x = 0.