Resonance of Solitons in One Dimension

Abstract

Resonances of solitons in one-dimensional space are studied theoretically taking the Sawada-Kotera equation with a nonvanishing boundary condition as an example. Two solitons near the resonant state exhibit the new phenomena. They interact with each other through emitting and absorbing third soliton. They are transmuted into singular solitons after colliding with each other. Two solitons at the resonant state fuse after colliding with each other, or a soliton splits into two solitons.