Wronskian and Gram Solutions to Integrable Equations using Bilinear Methods
2017
- 299Usage
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Citation Benchmarking is provided by Scopus and SciVal and is different from the metrics context provided by PlumX Metrics.
Metrics Details
- Usage299
- Downloads257
- Abstract Views42
Thesis / Dissertation Description
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.
Bibliographic Details
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