  We study the construction of analytical non-radially solutions for the
1-dimensional compressible adiabatic Euler equations in this article. We could
design the perturbational method to construct a new class of analytical
solutions. In details, we perturb the linear velocity:% \begin{equation}
u=c(t)x+b(t) \end{equation} and substitute it into the compressible Euler
equations. By comparing the coefficients of the polynomial, we could deduce the
corresponding functional differential system of
$(c(t),b(t),\rho^{\gamma-1}(0,t)).$ Then by skillfully applying the Hubble's
transformation: \begin{equation} c(t)=\frac{\dot{a}(t)}{a(t)}, \end{equation}
the functional differential equations can be simplified to be the system of
$(a(t),b(t),\rho^{\gamma-1}(0,t))$. After proving the existence of the
corresponding ordinary differential equations, a new class of blowup or global
solutions can be shown. Here, our results fully cover the previous known ones
by choosing $b(t)=0$.
