When is negativity not a problem for the ultradiscrete limit
When is negativity not a problem for the ultradiscrete limit
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对于超离散极限，什么时候负性不是问题
DOI：
10.1063/1.2360394
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发表时间：
2006
影响因子：
1.3
通讯作者：
S. Lafortune
中科院分区：
文献类型：
--
作者：
Alex M Kasman;S. Lafortune
“超离散极限”提供了可积差分方程和显示类孤子解的元胞自动机之间的联系。特别是，该过程通常将具有正系数的代数差分方程的严格正解转化为涉及“Max”算子的方程的相应解。尽管放弃这些正性条件肯定会造成潜在的困难，但即使不存在这些正性条件，解仍然有可能在超离散极限下持续存在。为了识别何时会发生这种情况，必须考虑某个表达式是否等于零，该表达式涉及差分方程中不同项及其系数的收敛率的度量。讨论的应用包括基本常差分方程的求解、Hirota 双线性差分方程的离散化以及超离散方程运动积分的识别。
The “ultradiscrete limit” has provided a link between integrable difference equations and cellular automata displaying soliton-like solutions. In particular, this procedure generally turns strictly positive solutions of algebraic difference equations with positive coefficients into corresponding solutions to equations involving the “Max” operator. Although it certainly is the case that dropping these positivity conditions creates potential difficulties, it is still possible for solutions to persist under the ultradiscrete limit, even in their absence. To recognize when this will occur, one must consider whether a certain expression, involving a measure of the rates of convergence of different terms in the difference equation and their coefficients, is equal to zero. Applications discussed include the solution of elementary ordinary difference equations, a discretization of the Hirota Bilinear Difference Equation and the identification of integrals of motion for ultradiscrete equations.
没有积极性的超离散化
DOI：
--
发表时间：
2006
期刊：
J. Phys. A : Math. Gen. Vol. 39
影响因子：
--
作者：
S.Kawashima;S.Nishibata;P.Zhu;S.Isojima
通讯作者：
S.Isojima
离散 Painleve 方程的极限和简并性
DOI：
--
发表时间：
2005
期刊：
Phys. A347
影响因子：
--
作者：
A.RAMANI;R.Willox;B.GRAMMATICOS;A.S.CARSTEA;Junkichi SATSUMA
通讯作者：
Junkichi SATSUMA