A construction of Multidimensional Dubrovin-Novikov Brackets
Ian A. B. Strachan
TL;DR
This paper presents a new method for constructing multi-dimensional, multi-component Dubrovin-Novikov brackets of hydrodynamic type, extending previous algebraic approaches using linear algebra techniques.
Contribution
It introduces an extended construction method based on Gelfand and Dorfman's work, enabling the generation of new examples of Dubrovin-Novikov brackets.
Findings
Provides a systematic construction approach
Extends previous algebraic frameworks
Facilitates the generation of multi-dimensional brackets
Abstract
A method for the construction of classes of examples of multi-dimensional, multi-component Dubrovin-Novikov brackets of hydrodynamic type is given. This is based on an extension of the original construction of Gelfand and Dorfman which gave examples of Novikov algebras in terms of structures defined from commutative, associative algebras. Given such an algebra, the construction involves only linear algebra.
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