  In this article, we study the perturbational method to construct the
non-radially symmetric solutions of the compressible 2-component Camassa-Holm
equations. In detail, we first combine the substitutional method and the
separation method to construct a new class of analytical solutions for that
system. In fact, we perturb the linear velocity: u=c(t)x+b(t), and substitute
it into the system. Then, by comparing the coefficients of the polynomial, we
can deduce the functional differential equations involving
$(c(t),b(t),\rho^{2}(0,t)).$ Additionally, we could apply the Hubble's
transformation c(t)={\dot{a}(3t)}/{a(3t)}, to simplify the ordinary
differential system involving $(a(3t),b(t),\rho ^{2}(0,t))$. After proving the
global or local existences of the corresponding dynamical system, a new class
of analytical solutions is shown. And the corresponding solutions in radial
symmetry are also given. To determine that the solutions exist globally or blow
up, we just use the qualitative properties about the well-known Emden equation:
{array} [c]{c} {d^{2}/{dt^{2}}}a(3t)= {\xi}{a^{1/3}(3t)}, a(0)=a_{0}>0
,\dot{a}(0)=a_{1} {array} . Our solutions obtained by the perturbational
method, fully cover the previous known results in "M.W. Yuen,
\textit{Self-Similar Blowup Solutions to the 2-Component Camassa-Holm
Equations,}J. Math. Phys., \textbf{51} (2010) 093524, 14pp." by the separation
method.
