The Study on the Theoretical Perspectives of Soliton and Its Applications

Abstract

Abstract: A soliton is a strongly stable, nonlinear, self-reinforcing, localised wave packet that propagates freely at a constant speed and keeps its shape even after colliding with other similar localised wave packets. Its exceptional stability arises from the balanced cancellation of nonlinear and dispersive effects in the medium. In engineering, a soliton wave is a self-reinforcing solitary wave packet that keeps its shape as it travels at a steady speed. It results from the medium's non-linear and dispersive effects cancelling each other out. Many systems exhibit dispersive effects, in which the wave frequency controls the wave's speed of propagation. It was then demonstrated that soliton solutions provide stable solutions for a wide class of dispersive partial differential equations that are weakly nonlinear and describe physical systems. Solitons are preferred for high-speed, longdistance transmissions because of their self-restoring characteristics. Given that transmission speeds over longer distances are now close to 40 Gbit per second, the strain on networks is rapidly approaching a critical threshold. Solitons may provide interesting alternatives in the future. Non-linear wave equations that describe how waves propagate in specific physical systems are solved to get soliton solutions. These waves appear as solutions in mathematical models of various systems, such as optical wave-guides, crystal lattice vibrations, and water waves.