New finite-gap solutions for the coupled Burgers equations engendered by the Neumann systems |
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| Authors: | Chen Jin-Bing Geng Xian-Guo Qiao Zhi-Jun |
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| Affiliation: | Department of Mathematics, Southeast University, Nanjing 210096, China; Department of Mathematics, Zhengzhou University, Zhengzhou 450052, China; Department of Mathematics, University of Texas–Pan American, Edinburg, TX 78541, USA |
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| Abstract: | ![]()
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. |
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| Keywords: | coupled Burgers equations Lax matrix Jacobi inversion finite-gap solutions |
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