A soliton is a localized travelling wave whose shape is preserved by the evolution and whose interactions with other solitons are elastic up to phase shifts.
An exact nonlinear-wave solution containing several localized solitons. In an integrable scattering solution, these objects approach separated incoming and outgoing profiles, with collision effects encoded by position shifts and internal phases. Bäcklund transformations and Hirota's bilinear method construct examples such as the Sine-Gordon multisoliton tau representation.
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A soliton is a self-reinforcing wave packet that maintains its shape while traveling at a constant speed. It is a special type of wave solution to certain nonlinear partial differential equations, characterized by its stability and ability to conserve its form over time and distance. Solitons are most commonly studied in the context of fluid dynamics, nonlinear optics, and various fields of physics and mathematics.