Wave Equation and Solitons

RM 216

The purpose of this research project was to investigate the nature of the wave equation as solitons and to produce models using the mathematical software Maple. Partial and ordinary differential equations that describe various linear and nonlinear wave were considered, solved, and modeled. Special attention was paid to finding and modeling the applications of solitons in the Korteweg-de Vries, Schrodinger, and Sine Gordon equations. Although solitons are used in a wide range of fields, the applications studied in this project were used to model waves in water. The models were then studied to promote a further understanding of the behavior of solitons in the forms of pulses, kinks, antikinks, breathers, bright solitons, and dark solitons.