Acta mathematica scientia,Series A ›› 2014, Vol. 34 ›› Issue (5): 1304-1312.

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Two Integrable Systems and Reductions

 GUO Xiu-Rong1, HU Mei-Yan2   

  1. 1.Department of Basic Courses, Shandong University of Science and Technology, Shandong Taian 271000;
    2.Department of Information Engineering, Shandong University of Science and Technology, Shandong Taian 271000
  • Received:2013-04-15 Revised:2014-07-08 Online:2014-10-25 Published:2014-10-25
  • Supported by:

    国家自然科学基金(11371361)、山东省自然科学基金(ZR2012AQ011)、山东省高等学校科技计划项目(J14LI58)和山东科技大学群星计划项目(QX2013143)资助

Abstract:

A Lie algebra is presented whose two corresponding loop algebras are followed to obtained, which are used to introduce two kinds of isospectral problems whose compatibility leads to two integrable dynamics. Some interesting nonlinear evolution equations are produced by reduction of the two dynamics, including the well-known Burgers equation, a generalized combined KdV-MKdV equation and the Kuramoto-Sivashinsky equation and a generalized form of the KdV equation. Then with the help of Bell polynomials we investigate some integrable properties of the generalized form of the KdV equation, such as bilinear representation, Lax pair, B"{a}cklund transformation, infinite conservation laws, and so on.

Key words: Integrable system,  B\"{a}cklund transformation, Bell polynomials

CLC Number: 

  • 35Q51
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