The WKIS System: Backlund Transformations, Generalized Fourier Transforms and All That : Astrophysics and Relativity

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概要

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• The spectral problem of Wadati-Konno-Ichikawa-Shimizu(WKIS) and the nonlinear evolution equations(NLEEs) related to it, which are solvable by the use of the inverse scattering method, are considered. The generating operators L_± and ∧_± of these NLEEs and of their Backlund transformations (BTs) together with the completeness relations of the eigenfunctions of both operators are derived. The action-angle variables and the hierarchies of Hamiltonian structures for these NLEE are constructed. The interrelations between the hierarchies of the WKIS system and its gauge equivalents (the Zakharov-Shabat system, etc.) are established. A convenient gauge transformation of the WKIS spectral problem is used to get in an alternative way the general BT. The so-called elementary BTs are obtained and it is shown that they can be cast into a form similar to that found by Darboux for the Schrodinger spectral problem. The nonlinear superposition formulae are also explicitly written.

• 理論物理学刊行会の論文
• 1986-05-25

著者

• PEMPINELLI F.

  Istituto Nazionale di Fisica Nucleare

• Boiti M

  Department Of Physics University Of Lecce

• Pempinelli F

  Department Of Physics University Of Lecce

• BOITI M.

  Department of Physics, University of Lecce

• GERDJIKOV V.S.

  Department of Physics, University of Lecce

• PEMPINELLI F.

  Department of Physics, University of Lecce

• Gerdjikov V.s.

  Department Of Physics University Of Lecce

関連論文

• The Nonlinear Evolution Equations Related to the Wadati-Konno-Ichikawa Spectral Problem
• The WKIS System: Backlund Transformations, Generalized Fourier Transforms and All That : Astrophysics and Relativity

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