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:% equation u=c(t)x+b(t) 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),ργ−1(0,t)). Then by skillfully applying the Hubble's transformation: equation c(t)=a(t)a(t), equation the functional differential equations can be simplified to be the system of (a(t),b(t),ργ−1(0,t))
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. 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