论文标题
Pearpeon模型中的可集成二次结构
Integrable quadratic structures in peakon models
论文作者
论文摘要
我们提出了三个可宽松的$ n $ n $ n $ peampon方程，camassa-holm，degasperis-procesi和novikov的lax表示的泊松结构的实现。源自连续方程的集成性结构的泊松结构产生了$ r $ -matrix表示的二次形式，而Toda Molecule Classical $ r $ -Matrix发挥了重要作用。 我们为$ r $ -matrix表示形式寻找线性形式。除了Camassa-Holm Case（在结构已经知道的情况下），其他两个案例不允许这样的演示，而Novikov模型的明显除外，$ n = 2 $。 在三种情况下，从规范的sklyanin痕量公式获得的普通汉密尔顿量。
We propose realizations of the Poisson structures for the Lax representations of three integrable $n$-body peakon equations, Camassa--Holm, Degasperis--Procesi and Novikov. The Poisson structures derived from the integrability structures of the continuous equations yield quadratic forms for the $r$-matrix representation, with the Toda molecule classical $r$-matrix playing a prominent role. We look for a linear form for the $r$-matrix representation. Aside from the Camassa--Holm case, where the structure is already known, the two other cases do not allow such a presentation, with the noticeable exception of the Novikov model at $n=2$. Generalized Hamiltonians obtained from the canonical Sklyanin trace formula for quadratic structures are derived in the three cases.
