The direct linearisation approach to hierarchies of integrable PDEs in 2 + 1 dimensions: I. Lattice equations and the differential-difference hierarchies
The direct linearisation approach to hierarchies of integrable PDEs in 2 + 1 dimensions: I. Lattice equations and the differential-difference hierarchies
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DOI：
10.1088/0266-5611/6/4/008
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发表时间：
1990-08
期刊：
影响因子：
2.1
通讯作者：
F. Nijhoff;H. Capel
中科院分区：
文献类型：
--
作者：
F. Nijhoff;H. Capel
利用直接线性化变换(DLT)方法对一族非线性发展方程进行了系统的研究。起始点是三维格子上的一类一般可积方程，其中变量取值于N*N矩阵的代数。从这些格子方程出发，通过适当的连续限制，作者得到了连续步骤的可积微分-差分方程组和偏微分方程组。它们将自己限制在连续统极限，从而得到具有一个连续(时间)变量和两个离散晶格演化变量的方程。
Using the direct linearising transform (DLT) method a systematic study is undertaken of hierarchies of nonlinear evolution equations. The starting point is a general class of integrable equations on a three-dimensional lattice where the variables take values in the algebra of N*N matrices. From these lattice equations by performing suitable continuum limits the authors obtain hierarchies of integrable differential-difference and partial differential equations in successive steps. They restrict themselves to continuum limits leading to equations with one continuous (time) variable and two discrete lattice evolution variables.