Differential-algebraic solutions of the heat equation
  In this work we introduce the notion of differential-algebraic ansatz for the heat equation and explicitly construct heat equation and Burgers equation solutions given a solution of a homogeneous non-linear ordinary differential equation of a special form. The ansatz for such solutions is called the $n$-ansatz, where $n+1$ is the order of the differential equation. 
Victor M. Buchstaber, Elena Yu. Netay
math-ph math.DS math.MP