On the tangent bundle TSN-1 of the unit sphere SN-l, 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...On the tangent bundle TSN-1 of the unit sphere SN-l, 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.展开更多
基金supported by the Scientific Foundation of the Southeast University of China (Grant No.KJ2009359)the National Natural Science Foundation of China (Grant No.10871182)+1 种基金the U.S.Army Research Office (contract/grant number W911NF-08-1-0511)Texas grant NHARP 2010
文摘On the tangent bundle TSN-1 of the unit sphere SN-l, 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.
