TITLE:
Embedded Vector Solitons
AUTHORS:
Jorge Fujioka, Rosalío Fernando Rodríguez
KEYWORDS:
Embedded Solitons, Vector Solitons, Nonlinear Schrödinger Equation, Complex Modified Korteweg-de Vries Equation
JOURNAL NAME:
Applied Mathematics,
Vol.16 No.8,
August
7,
2025
ABSTRACT: 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.