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New finite-gap solutions for the coupled Burgers equations engendered by the Neumann systems
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On the tangent bundle TSN-1 of the unit sphere SN-1, this paper reduces the coupled Burgers equations to two Neumann systems by using the nonlinearization of the Lax pair, whose Liouville integrability is displayed in the scheme of the r-matrix technique. Based on the Lax matrix of the Neumann systems, the Abel--Jacobi coordinates are appropriately chosen to straighten out the restricted Neumann flows on the complex torus, from which the new finite-gap solutions expressed by Riemann theta functions for the coupled Burgers equations are given in view of the Jacobi inversion. 相似文献
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This paper is devoted to the study of the underlying linearities of the coupled
Harry--Dym (cHD) soliton hierarchy, including the well-known cHD equation. Resorting
to the nonlinearization of Lax pairs, a family of finite-dimensional Hamiltonian
systems associated with soliton equations are presented, constituting the
decomposition of the cHD soliton hierarchy. After suitably introducing the
Abel--Jacobi coordinates on a Riemann surface, the cHD soliton hierarchy can be
ultimately reduced to linear superpositions,
expressed by the Abel--Jacobi variables. 相似文献
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Two (2 1)-dimensional (3D) lattice systems are proposed in view of the compatibility of 2D lattice systems in the same hierarchy. Furthermore, the Darboux transformation (DT) method is generalized to the case of 3D lattice equations. As a consequence, some exact solutions for the resulting discrete systems are presented. 相似文献
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