Open Access. Powered by Scholars. Published by Universities.®
Numerical Analysis and Computation Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 1 of 1
Full-Text Articles in Numerical Analysis and Computation
Asymptotic And Numerical Analysis Of Coherent Structures In Nonlinear Schrodinger-Type Equations, Cory Ward
Asymptotic And Numerical Analysis Of Coherent Structures In Nonlinear Schrodinger-Type Equations, Cory Ward
Doctoral Dissertations
This dissertation concerns itself with coherent structures found in nonlinear Schrödinger-type equations and can be roughly split into three parts. In the first part we study a deformation of the defocusing nonlinear Schrödinger (NLS) equation, the defocusing Camassa-Holm NLS (CH-NLS) equation in both one and two space dimensions. We use asymptotic multiscale expansion methods to reduce this model to a Boussinesq-like equation, which is then subsequently used to obtain approximate solitary wave solutions for both the 1D and 2D CH-NLS equations. We then use direct numerical simulations to investigate the validity of these approximate solutions, their evolution, and their head-on …