Nonlocality, integrability, and solitons

Abstract

We explore integrable equations that involve involution points, along with the solution phenomena for Cauchy problems associated with nonlocal differential equations. By applying group reductions to classical Lax pairs, we generate nonlocal integrable equations. Soliton solutions of these models are derived using binary Darboux transformations or reflectionless Riemann–Hilbert problems in the nonlocal context. Further discussion on the well-posedness of nonlocal differential equations is also presented.