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The nonlinear evolution equations related to the Wadati-Konno-Ichikawa spectral problem. (English) Zbl 1200.45003
Summary: The Wadati-Konno-Ichikawa (WKI) spectral problem is considered and the nonlinear evolution equations (NLEE) related to this problem are explicitly constructed. Together with the integrable NLEE already found by WKI new pure differential solvable NLEEs are derived. The properties of the integro-differential operator $$L$$ generating all the considered NLEEs are studied. It is shown that the usually successful procedure used to derive the Bäcklund transformation does not work with these highly nonlinear evolution equations.

##### MSC:
 45K05 Integro-partial differential equations 35Q53 KdV equations (Korteweg-de Vries equations) 35A30 Geometric theory, characteristics, transformations in context of PDEs
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