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Journal of Mathematical Physics / Volume 52 / Issue 9 / ARTICLES / PDE and Applied Mathematics

J. Math. Phys. 52, 093704 (2011); http://dx.doi.org/10.1063/1.3633526 (33 pages)

Twisted hierarchies associated with the generalized sine-Gordon equation

Hui Ma1 and Derchyi Wu2

1Department of Mathematical Sciences, Tsinghua University, Beijing 100084, People's Republic of China
2Institute of Mathematics, Academia Sinica, Taipei 10617, Taiwan

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(Received 11 April 2011; accepted 15 August 2011; published online 14 September 2011)

Twisted U- and twisted U/K-hierarchies are soliton hierarchies introduced by Terng to find higher flows of the generalized sine-Gordon equation. Twisted math-hierarchies are among the most important classes of twisted hierarchies. In this paper, we derive explicit interesting first and higher flows of twisted math-hierarchies, justify that the one-dimensional systems of twisted math-hierarchies for J = Iq, n − q(1 ⩽ q ⩽ n − 1), called the generalized sinh-Gordon equations, are the Gauss-Codazzi equations for n-dimensional timelike submanifolds with constant sectional curvature 1 and index q in pseudo-Euclidean (2n − 1)-dimensional space math2q−12n−1 with index 2q − 1. Furthermore, a unified treatment of the inverse scattering theory for twisted math-hierarchies is provided.

© 2011 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. THE TWISTED math -HIERARCHY
  3. THE ONE-DIMENSIONAL SYSTEM
  4. THE DIRECT SCATTERING PROBLEM
  5. THE INVERSE SCATTERING PROBLEM I
  6. THE INVERSE SCATTERING PROBLEM II
  7. THE CAUCHY PROBLEM

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KEYWORDS and PACS

Keywords

differential geometry, partial differential equations, sine-Gordon equation, solitons

PACS

  • 02.40.Hw

    Classical differential geometry

  • 02.30.Jr

    Partial differential equations

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3633526

PUBLICATION DATA

ISSN

0022-2488 (print)  
1089-7658 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

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