In mathematics and physics, a soliton is a self-reinforcing solitary wave (a wave packet or pulse) that maintains its shape while it travels at constant speed. Solitons are caused by a cancellation of non-linear and dispersive effects in the medium. "Dispersive effects" refer to dispersion relations between the frequency and the speed of the waves. Solitons arise as the solutions of a widespread class of weakly non-linear dispersive partial differential equations describing physical systems. This book presents the latest research in the field.