Belov–Chaltikian and Blaszak–Marciniak lattice equations: Recursion operators and factorization
Belov–Chaltikian and Blaszak–Marciniak lattice equations: Recursion operators and factorization
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DOI：
10.1063/1.1530755
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发表时间：
2003-01
影响因子：
1.3
通讯作者：
R. Sahadevan;S. Khousalya
中科院分区：
文献类型：
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作者：
R. Sahadevan;S. Khousalya
利用广义对称性，系统地研究了两个独立变量（一个连续变量，一个离散变量）的偏微分差分方程（PDDEs）的递归算子的构造.并说明了如何因式分解所得到的递归算子。对相对论性户田（RT）、Belov-Chaltikian（BC）和Blaszak-Marciniak（BM）格点方程，说明了上述方法的适用性，并指出前两种格点方程允许（2×2）矩阵递归算子，而后者具有（3×3）矩阵递归算子.此外，所构造的递归算子可以被写为每个格方程中的2个不同的可逆矩阵算子的因子。本文还明确地证明了因式分解算子是Hamilton的，从而RT、BC和BM格点方程是双Hamilton系统。
A systematic investigation on the construction of recursion operators for partial differential–difference equations (PDDEs) with two independent variables (one continuous and one discrete) using its generalized symmetries is presented. Also it is explained how to factorize the obtained recursion operators. The applicability of the above procedure have been illustrated for the relativistic toda (RT), Belov–Chaltikian (BC) and Blaszak–Marciniak (BM) lattice equations and shown that the former two lattice equations admit (2×2) matrix recursion operators while the latter one possesses a (3×3) matrix recursion operator. Furthermore, the constructed recursion operators can be written as a factor of 2 distinct invertible matrix operators in each of the lattice equations. It is also proved explicitly that the factorized operators are Hamiltonian and hence RT, BC and BM lattice equations are bi-Hamiltonian systems.