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Prog. Theor. Phys. Vol. 75 No. 5 (1986) pp. 1111-1141

[ Full Text PDF : FREE ACCESS (1359K) ]

The WKIS System: Bäcklund Transformations, Generalized Fourier Transforms and All That

M. Boiti, V. S. Gerdjikov and F. Pempinelli

Department of Physics, University of Lecce, 73100 Lecce

(Received August 29, 1985)

Abstract:

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 A± of these NLEEs and of their Bäcklund 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 Schrödinger spectral problem. The nonlinear superposition formulae are also explicitly written.


URL : http://ptp.ipap.jp/link?PTP/75/1111/
DOI : 10.1143/PTP.75.1111

[ Full Text PDF : FREE ACCESS (1359K) ] Citation:

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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 128 No. 5 (2012) pp. 993-999 :
    Exact Stationary Solution Method for the Wadati-Konno-Ichikawa-Shimizu (WKIS) Equation
    Robert A. Van Gorder

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