The bi‐Hamiltonian formulation of the Landau–Lifshiftz equation
The bi‐Hamiltonian formulation of the Landau–Lifshiftz equation
复制标题
Landau-Lifshiftz 方程的双哈密顿公式
DOI：
10.1063/1.528053
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发表时间：
1988
影响因子：
1.3
通讯作者：
V. Papageorgiou
中科院分区：
文献类型：
--
作者：
E. Barouch;A. Fokas;V. Papageorgiou
Landau-Lifshitz（LL）方程是可积磁系统的普遍模型。它包含正弦戈登（SG），非线性薛定谔（NLS）和海森堡模型（HM）方程作为特殊或限制情况。众所周知，NLS、SG和HM方程都具有递归运算符。哈密顿形式的方程的递归算子生成（a）可积方程的族，和（B）第二哈密顿算子和更一般地泊松结构的族。这里通过算法得到LL方程的递归算子，从而建立其双哈密顿公式。
The Landau–Lifshitz (LL) equation is a universal model for integrable magnetic systems. It contains the sine–Gordon (SG), nonlinear Schrodinger (NLS), and the Heisenberg model (HM) equations as particular or limiting cases. It is well known that the NLS, SG, and HM equations possess recursion operators. A recursion operator of an equation in Hamiltonian form generates (a) a hierarchy of integrable equations, and (b) a second Hamiltonian operator and more generally a hierarchy of Poisson structures. Here the recursion operator of the LL equation is obtained algorithmically, and hence its bi‐Hamiltonian formulation is established.