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Solitons are self-reinforcing, localized wave packets that maintain their shape while they propagate at a constant velocity. They arise in nonlinear systems and are a fundamental concept in various fields of physics and mathematics. Unlike linear waves, which tend to disperse and spread out over time, solitons exhibit remarkable stability. This stability arises from a delicate balance between the nonlinear effects that tend to steepen the wave and dispersive effects that tend to broaden it. When these opposing forces are precisely matched, the wave can travel indefinitely without changing its form.

The term "soliton" was coined by physicist Norman Zabusky in 1965, who observed these stable, particle-like waves in numerical simulations of the Korteweg-de Vries (KdV) equation. The KdV equation describes phenomena such as shallow water waves and plasma waves. Since their discovery, solitons have been found to exist in a wide range of nonlinear systems, including optical fibers, Bose-Einstein condensates, and certain biological systems. Their particle-like behavior and resistance to dispersion make them ideal candidates for transmitting information over long distances with minimal degradation. The study of solitons continues to be an active area of research, with ongoing investigations into their properties and potential applications.