Similarity ansatz
= Similarity ansatz
{title2=$u(x,t)=t^\alpha F(x/t^\beta)$}
A similarity ansatz assumes a profile invariant under a prescribed rescaling, commonly in the displayed power-law form. Substitution into a <partial differential equation> fixes compatible exponents and can reduce it to an <ordinary differential equation> for $F$. Boundary conditions and conserved quantities must also be compatible with the scaling; the ansatz alone does not establish existence of a solution.