In this paper we present an algorithm to find the discrete Lagrangian for an autonomous recurrence relation of arbitrary even order 2k with k > 1. The method is based on the existence of a set of differential operators called annihilation operators which can be used to convert a functional equation into a system of linear partial differential equations. This completely solves the inverse problem of the calculus of variations in this setting.
On the inverse problem of the discrete calculus of variations / G. Gubbiotti. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL. - ISSN 1751-8113. - 52:30(2019), pp. 305203.1-305203.29. [10.1088/1751-8121/ab2919]
On the inverse problem of the discrete calculus of variations
G. Gubbiotti
2019
Abstract
In this paper we present an algorithm to find the discrete Lagrangian for an autonomous recurrence relation of arbitrary even order 2k with k > 1. The method is based on the existence of a set of differential operators called annihilation operators which can be used to convert a functional equation into a system of linear partial differential equations. This completely solves the inverse problem of the calculus of variations in this setting.
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