During my research I performed some numerics and videos. These simulations train our intuition about the dynamics of the PDE. Also in Youtube one can find some interesting real experiments and their results.
Example 1:
Example 2:
Example 3:
KSPE11 corresponds to β identically a constant; KSPE12 corresponds to β(x)=x; KSPE21 corresponds to β(x)=x2; KSPE22 corresponds to β(x)=log(1+x)
KSPP11 corresponds to β = α =1; KSPP12 corresponds to β= 2, α=1.5; KSPP21 corresponds to α=β=1.5; KSPP22 corresponds to α=1.75, β=2
BL1 corresponds to ν=0, μ=0.5 and β=1; BL2 corresponds to ν=0.5, α=0.5, μ=0.5 and β=0.5
KS1 corresponds to γ=1, δ=1, ε=0.01; KS2 corresponds to ε=0.8, δ=0.5, γ=1.45