The soliton solutions for the Wadati-Konno-Ichikawa equation.

By taking the Wadati–Konno–Ichikawa (WKI) equation as an example, this paper refines the Olmedilla’s technique of solving the Gelfand–Levitan–Marchenko (GLM) equation with one higher-order pole. In order to solve the GLM equation, the Laurent’s series and residue theorem are used, and the formulae of the Nth order soliton solution and Nth order bound-state soliton solution are expressed in a unified determinant form. Moreover, these formulae are simpler and more explicit to calculate solutions of the nonlinear integrable equations, compared with the results of Olmedilla.