The nonlinear evolution equations related to the Wadati-Konno-Ichikawa spectral problem. (English) Zbl 1200.45003

Boiti, M.; Pempinelli, F.; Tu, Guizhang

Prog. Theor. Phys. 69, No. 1, 48-64 (1983).

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