Symmetry broken and symmetry preserving multi-soliton solutions for nonlocal complex short pulse equation

Abstract

Abstract In this article we consider a general system of complex short pulse equation (CSPE) that under certain nonlocal symmetry reduction yields a reverse space-time nonlocal complex short pulse equation (NL-CSPE). We apply matrix Darboux transformation to the associated Lax pair and construct multi-soliton solutions. K-soliton solution is expressed in terms of quasideterminant formula which enable us to compute explicit expressions of symmetry broken and symmetry preserving one- and two-soliton solutions for NL-CSPE. In addition to these solutions, we also obtain one-bright and interaction of two-bright solitons for classical CSPE. All these investigations end up with the conclusion that both symmetry preserving and broken solutions exist for NL-CSPE.