arXiv subjects

B. Kent Harrison

Publications and source records attributed to B. Kent Harrison.

3 recordsLinked to original sources

arXiv2023

Backlund-Transformation-Related Recursion Operators: Application to the Self-Dual Yang-Mills Equation

By using the self-dual Yang-Mills (SDYM) equation as an example, we study a method for relating symmetries and recursion operators of two partial differential equations connected to each other by a non-auto-Backlund transformation. We prove the Lie-algebra isomorphism between the symmetries of the SDYM equation and those of the potential SDYM (PSDYM) equation, and we describe the construction of the recursion operators for these two systems. Using certain known aspects of the PSDYM symmetry algebra, we draw conclusions regarding the Lie algebraic structure of the "potential symmetries" of the SDYM equation.

math-ph↗

arXiv2009

A Method for Constructing a Lax Pair for the Ernst Equation

A systematic construction of a Lax pair and an infinite set of conservation laws for the Ernst equation is described. The matrix form of this equation is rewritten as a differential ideal of gl(2,R)-valued differential forms, and its symmetry condition is expressed as an exterior equation which is linear in the symmetry characteristic and has the form of a conservation law. By means of a recursive process, an infinite collection of such laws is then obtained, and the conserved "charges" are used to derive a linear exterior equation whose components constitute a Lax pair.

math-ph↗

arXiv2005

The Differential Form Method for Finding Symmetries

This article reviews the use of differential forms and Lie derivatives to find symmetries of differential equations, as originally presented by Harrison and Estabrook, J. Math. Phys., 12 (1971), 653. An outline of the method is given, followed by examples and references to recent papers using the method.

math-ph↗