Bäcklund transformation and soliton solutions for a generalized Wadati-Konno-Ichikawa equation

By employing a reciprocal transformation, we relate the generalized Wadati–Konno–Ichikawa (gWKI) equation to an associated gWKI (agWKI) equation. Utilizing the Darboux transformation of the agWKI equation and Bianchi's theorem of permutability, we derive the $ N $-Bäcklund transformation for the gWKI equation. As an application, we obtain some soliton solutions for the gWKI equation, including smooth solitons, bursting solitons, and loop-type solitons. Furthermore, we explore the interactions between two solitons.