  In this work, the generalized $N$-component Fokas-Lenells(FL) equations,
which have been studied by Guo and Ling (2012 J. Math. Phys. 53 (7) 073506) for
$N=2$, are first investigated via Riemann-Hilbert(RH) approach. The main
purpose of this is to study the soliton solutions of the coupled
Fokas-Lenells(FL) equations for any positive integer $N$, which have more
complex linear relationship than the analogues reported before. We first
analyze the spectral analysis of the Lax pair associated with a $(N+1)\times
(N+1)$ matrix spectral problem for the $N$-component FL equations. Then, a kind
of RH problem is successfully formulated. By introducing the special conditions
of irregularity and reflectionless case, the $N$-soliton solution formula of
the equations are derived through solving the corresponding RH problem.
Furthermore, take $N=2,3$ and $4$ for examples, the localized structures and
dynamic propagation behavior of their soliton solutions and their interactions
are discussed by some graphical analysis.
