In this article, we study the self-similar solutions of the 2-component Degasperis-Procesi water system:% [c]c% ρ_t+k₂uρ_x+(k₁+k₂)ρu_x=0 u_t-u_xxt+4uu_x-3u_xu_xx-uu_xxx+k₃ρρ_x=0. By the separation method, we can obtain a class of self-similar solutions,% [c]c% ρ(t,x)=(f(η)a(4t)^(k₁+k₂)/4,0),u(t,x)=·a(4t)a(4t)x ··a(s)-ξ4a(s)^κ=0,a(0)=a₀% ≠0,·a(0)=a₁ f(η)=k₃ξ√-ξk₃η²+(ξk₃α) ²% where η=a(s)1/4x with s=4t;
Nearby in the stack
κ=2k1
α≥0,
ξ<0
,
a0
and
a1
are constants. which the local or global behavior can be determined by the corresponding Emden equation. The results are very similar to the one obtained for the 2-component Camassa-Holm equations. Our analytical solutions could provide concrete examples for testing the validation and stabilities of numerical methods for the systems. With the characteristic line method, blowup phenomenon for