A nontrivial behaviour of a nonlinear wave under influence of small disturbing factors like dissipation, smooth inhomogeneity of medium parameters, etc. is considered by the example of sine-Gordon equation. The stage of slow "adiabatic" variation of the parameters of quasi-stationary wave is shown to change at some finite distance due to strong instability. The wave form becomes essentially non-stationary (breaking of stationary wave structure). The breaking condition is defined by the extremum of the wave adiabatic invariant. The behaviour of a wave at the nonadiabatic stage is described using a Galerkin procedure. © 1981.
Pelinovsky, E. N., & Shavratsky, S. K. (1981). Breaking of solitary and periodic nonlinear waves. Physica D: Nonlinear Phenomena, 3(1–2), 410–419. https://doi.org/10.1016/0167-2789(81)90144-5