Dromion solutions of noncommutative Davey-Stewartson equations
Claire R. Gilson, Susan R. Macfarlane
TL;DR
This paper develops noncommutative Davey-Stewartson equations, derives quasideterminant solutions using Darboux transformations, and computes dromion solutions with visualizations, advancing understanding of noncommutative integrable systems.
Contribution
It introduces noncommutative Davey-Stewartson equations and constructs explicit quasideterminant solutions, including dromion solutions, using Darboux transformations.
Findings
Derived quasideterminant solutions verified by substitution
Computed and visualized noncommutative dromion solutions
Extended integrable systems theory to noncommutative settings
Abstract
We consider a noncommutative version of the Davey-Stewartson equations and derive two families of quasideterminant solution via Darboux and binary Darboux transformations. These solutions can be verified by direct substitution. We then calculate the dromion solutions of the equations and obtain computer plots in a noncommutative setting.
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