Quasi-periodic solutions of the negative-order Jaulent–Miodek hierarchy
Quasi-periodic solutions of the negative-order Jaulent–Miodek hierarchy
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DOI：
10.1142/s0129055x20500075
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发表时间：
2019-06
影响因子：
1.8
通讯作者：
Jinbing Chen
中科院分区：
文献类型：
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作者：
Jinbing Chen
利用一类后向Neumann型系统给出了负阶Jaulent-Miodek（nJM）族拟周期解的统一构造.从后向Lenard梯度出发，将nJM族置于零曲率的设置中，并得到双Hamilton结构，从而显示出其可积性。将Lax对的非线性化推广到nJM族，使其可化为一列后向Neumann型系统，其对合解产生nJM族的有限参数解.给出了负阶定常JM方程，给出了nJM流的有限维不变子空间。与由Lax矩阵确定的谱曲线，nJM流的Jacobi各种黎曼曲面上线性化。最后，将Riemann-Jacobi反演应用于nJM流的Abel-Jacobi解，得到了nJM族的拟周期解.
A uniform construction of quasi-periodic solutions to the negative-order Jaulent–Miodek (nJM) hierarchy is presented by using a family of backward Neumann type systems. From the backward Lenard gradients, the nJM hierarchy is put into the zero-curvature setting and the bi-Hamiltonian structure displaying its integrability. The nonlinearization of Lax pair is generalized to the nJM hierarchy such that it can be reduced to a sequence of backward Neumann type systems, whose involutive solutions yield finite parametric solutions of the nJM hierarchy. The negative [Formula: see text]-order stationary JM equation is given to specify a finite-dimensional invariant subspace for the nJM flows. With a spectral curve determined by the Lax matrix, the nJM flows are linearized on the Jacobi variety of a Riemann surface. Finally, the Riemann–Jacobi inversion is applied to Abel–Jacobi solutions of the nJM flows, by which some quasi-periodic solutions are obtained for the nJM hierarchy.