1A)Find the similarity structure of the fundamental solution to the following one dimensional non-linear diffusion equation and suggest a functional form of the solution: u_xx − uu_t = δ(x)δ(t), −∞ < x < ∞, 0 ≤ t < ∞,
u(x, t) = 0, as |x| → ∞,
u(x, 0) = 0.
1b) Choose a suitable similarity variable based on your answer above and derive the ordinary differential equation in terms of the similarity variable. (please solve it using any boundary condition)