Exact Solutions to Nonlinear Partial Differential Equations: Soliton and Different Types of Solutions

Abstract

Nonlinear partial differential equations (PDEs) are central to modeling complex phenomena in physics, engineering, and applied mathematics, from fluid dynamics to optical solitons. Although numerical and approximate methods are the most common methods, exact solutions remain crucial. Integrable systems, such as the Korteweg–de Vries (KdV) and Kadomtsev–Petviashvili (KP) equations, have revolutionized soliton theory, yet higher-dimensional and generalized nonlinear PDEs remain underexplored. This research advances techniques such as Hirota’s bilinear formalism and Wronskian determinant techniques to systematically derive and classify exact solutions.

Date of Award	2025
Original language	American English
Supervisor	Alrazi Abdeljabbar (Supervisor)