In magnets, there also exist different types of solitons and other nonlinear waves.

He retired in 1981 but continued to work on nonlinear waves.

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

Self-similarities, nonlinear waves and intermediate asymptotics.

Stokes already identified two possible definitions of phase velocity for periodic nonlinear waves:

The KdV equation is an asymptotic model of the propagation of nonlinear dispersive waves.

Unlike solitons (another kind of nonlinear wave), the energy of a shock wave dissipates relatively quickly with distance.

While the KdV or Boussinesq models give good approximations for these long nonlinear waves.

Higher-order cnoidal wave theories remain valid for shorter and more nonlinear waves.

This corresponds with the longer and more nonlinear waves.