A Numerical and Analytical Investigation of The sine-Gordon Equation and Its Soliton Solutions

Abstract: This thesis investigates the nonlinear partial differential equation known as sine-Gordon and its special soliton solutions.Simpler analytical results are derived and more advanced methods and their results are discussed.Further, a finite difference scheme is derived, implemented and compared against a known energy conserving scheme of sine-Gordon in terms of stability, accuracy, convergence and computation time.The complete solvability of the equation enables comparison between numerical solutions and their analytical counterparts.No unified answer to which numerical scheme is best was determined as they both were shown to have pros and cons.