$N$-soliton formula and blowup result of the Wadati-Konno-Ichikawa equation

Abstract

We formulate the $N$ soliton solution of the Wadati-Konno-Ichikawa equation that is determined by purely algebraic equations. Derivation is based on the matrix Riemann-Hilbert problem. We give examples of one soliton solution that include smooth soliton, bursting soliton, and loop type soliton. In addition, we give an explicit example for two soliton solution that blows up in a finite time.