Subcategory: Physics (not Nanoscience)
Samuel Uba - Alabama A&M University
Co-Author(s): Dr. Matthew Edwards, Alabama A&M University Huntsville, AL
This research investigates and compares analytical and numerical soliton solutions of the coupled nonlinear Klein-Gordon Equations. Both cubic and higher power law nonlinearities have been considered. Numerical calculations have been implemented using Finite Element Methods and Mathematica, and results have been compared with analytical outcomes. Variational iteration methods were used to perform integrations. The Klein-Gordon equation is the relativistic limit of the Schrodinger equation in zero spin quantum systems. To that extent, its importance and nonlinear extension, as is the case when the potential energy operator depends on the wavefunction, are considered paramount for subsequent density functional calculations in condensed matter physics.Not Submitted
Funder Acknowledgement(s): NSF-RISE
Faculty Advisor: Dr Matthew Edwards, email@example.com
Role: Solve analytical and numerical coupled nonlinear Klein-Gordon equation.