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In mathematics, the Volterra lattice, also known as the discrete KdV equation, the Kac–van Moerbeke lattice, and the Langmuir lattice, is a system of ordinary differential equations with variables indexed by some of the points of a 1-dimensional lattice. It was introduced by and and is named after Vito Volterra. The Volterra lattice is a special case of the generalized Lotka–Volterra equation describing predator–prey interactions, for a sequence of species with each species preying on the next in the sequence. The Volterra lattice also behaves like a discrete version of the KdV equation. The Volterra lattice is an integrable system, and is related to the Toda lattice. It is also used as a model for Langmuir waves in plasmas. ==Definition== The Volterra lattice is the set of ordinary differential equations for functions ''a''''n'': :''a''''n''' = ''a''''n''(''a''''n''+1 – a''n''–1) where ''n'' is an integer. Usually one adds boundary conditions: for example, the functions ''a''''n'' could be periodic: ''a''''n'' = ''a''''n''+''N'' for some ''N'', or could vanish for ''n'' ≤ 0 and ''n'' ≥ ''N''. The Volterra lattice was originally stated in terms of the variables ''R''''n'' = –log ''a''''n'' in which case the equations are : ''R''''n''' = e−''R''''n''–1 – e−''R''''n''+1 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Volterra lattice」の詳細全文を読む スポンサード リンク
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