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

TL;DR

This paper derives explicit N-soliton solutions for the Wadati-Konno-Ichikawa equation using algebraic and Riemann-Hilbert methods, and demonstrates finite-time blowup phenomena.

Contribution

It introduces a new algebraic formulation of N-soliton solutions and provides explicit examples including blowup behavior.

Findings

Explicit N-soliton solutions derived

Examples include smooth, bursting, and loop solitons

Finite-time blowup demonstrated in two-soliton case

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.