Gradient-Induced Fission of Solitons

A theory of nonlinear dispersive-wave propagation in inhomogeneous media is used to predict the behavior of a Korteweg-de Vries solitary wave (soliton) incident on a gradient region between two uniform regions. When the gradient induces a transition into an unstable state, the soliton fissions into a train of solitons plus, in general, an oscillatory tail. We derive formulas giving the number and amplitudes of the fission solitons. The theory is applied to surface gravity waves, magnetosonic waves, and ion-acoustic waves.