The soliton solutions for the Wadati–Konno–Ichikawa equation

Abstract

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.