Wronskian and Gram Solutions to Integrable Equations using Bilinear Methods

Author

Benjamin Wiggins, University of VermontFollow

Date of Award

2017

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

First Advisor

Jianke Yang

Abstract

This thesis presents Wronskian and Gram solutions to both the Korteweg-de Vries and Kadomtsev-Petviashvili equations, which are then scalable to arbitrarily large numbers of interacting solitons.

Through variable transformation and use of the Hirota derivative, these nonlinear partial differential equations can be expressed in bilinear form. We present both Wronskian and Gram determinants which satisfy the equations.

N=1,2,3 and higher order solutions are presented graphically; parameter tuning and the resultant behavioral differences are demonstrated and discussed. In addition, we compare these solutions to naturally occurring shallow water waves on beaches.

Language

en

Number of Pages

45 p.

Recommended Citation

Wiggins, Benjamin, "Wronskian and Gram Solutions to Integrable Equations using Bilinear Methods" (2017). Graduate College Dissertations and Theses. 751.
https://scholarworks.uvm.edu/graddis/751