Scaling, Self-similarity and Superposition

Abstract

A novel procedure for the nonlinear superposition of two self-similar solutions of the heat conduction equation with power-law nonlinearity is introduced. It is shown how the boundary conditions of the superposed state conflicts with self-similarity, rendering the nonlinearly superposed state to be a non-exact solution. It is argued that the nonlinearity couples with the presence of the scale so that the superposition in the linear case can give an exact solution.