Solitary waves are waveforms that maintain their shape while traveling at a constant speed. Unlike regular waves that can spread out and lose energy, solitary waves can exist in various mediums, such as water or plasma. They are often described as "solitons" when they arise in nonlinear systems, where the wave's speed depends on its amplitude. These waves are significant in fields like fluid dynamics and nonlinear optics, as they can model phenomena such as tsunamis or light pulses in fiber optics. Their stability and persistence make them a fascinating subject of study in both theoretical and applied physics.