Embedded Vector Solitons

In this article, we demonstrate that embedded vector solitons (EVSs) indeed exist. In other words, we prove that there exist systems of nonlinear partial differential equations (NLPDEs) which have soliton solutions ( u,v ) , where each of the solitons, u( z,t ) and v( z,t ) , is an embedded soliton. We present two systems of NLPDEs with these peculiar EVSs: a system of two cubic-quintic nonlinear Schrödinger (NLS) equations, and a system of two complex modified Korteweg-de Vries (cmKdV) equations. These two systems are the first systems of NLPDEs with EVSs known to date. Moreover, we demonstrate that these two systems also possess dark vector solitons and a highly unusual type of vector soliton: mixed vector solitons, which are composed of a bright soliton and a dark one.