Physics
Scientific paper
May 1986
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986pthph..75.1111b&link_type=abstract
Progress of Theoretical Physics, Vol. 75, No. 5, pp. 1111-1141
Physics
3
Scientific paper
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.
Boiti Marco
Gerdjikov Vladimir S.
Pempinelli Flora
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