The Riccati System and a Diffusion-Type Equation
  We discuss a method of constructing solution of the initial value problem for duffusion-type equations in terms of solutions of certain Riccati and Ermakov-type systems. A nonautonomous Burgers-type equation is also considered. 
Erwin Suazo, Sergei K. Suslov and Jose M. Vega-Guzman
math-ph math.MP