中国物理B ›› 2010, Vol. 19 ›› Issue (9): 90403-090403.doi: 10.1088/1674-1056/19/9/090403

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New finite-gap solutions for the coupled Burgers equations engendered by the Neumann systems

陈金兵1, 乔志军2, 耿献国3   

  1. (1)Department of Mathematics, Southeast University, Nanjing 210096, China; (2)Department of Mathematics, University of Texas -- Pan American, Edinburg, TX 78541, USA; (3)Department of Mathematics, Zhengzhou University, Zhengzhou 450052, China
  • 收稿日期:2010-01-02 修回日期:2010-03-06 出版日期:2010-09-15 发布日期:2010-09-15
  • 基金资助:
    Project supported by the Scientific Foundation of the Southeast University of China (Grant No. KJ2009359), the National Natural Science Foundation of China (Grant No. 10871182) and the U. S. Army Research Office (contract/grant number W911NF-08-1-0511) an

New finite-gap solutions for the coupled Burgers equations engendered by the Neumann systems

Chen Jin-Bing(陈金兵)a)†, Geng Xian-Guo(耿献国)b), and Qiao Zhi-Jun(乔志军)c)   

  1. a Department of Mathematics, Southeast University, Nanjing 210096, China; b Department of Mathematics, Zhengzhou University, Zhengzhou 450052, China; c Department of Mathematics, University of Texas–Pan American, Edinburg, TX 78541, USA
  • Received:2010-01-02 Revised:2010-03-06 Online:2010-09-15 Published:2010-09-15
  • Supported by:
    Project supported by the Scientific Foundation of the Southeast University of China (Grant No. KJ2009359), the National Natural Science Foundation of China (Grant No. 10871182) and the U. S. Army Research Office (contract/grant number W911NF-08-1-0511) and Texas grant NHARP 2010.

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摘要： 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.

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.

Key words: coupled Burgers equations, Lax matrix, Jacobi inversion, finite-gap solutions

中图分类号: 

  • 0420J