Scaling, Self-similarity and Superposition

Details Scaling, Self-similarity and Superposition Scaling, Self-similarity and Superposition

2009-08-24

arxiv.org/abs/0908.3337v2

Physics

Mathematical Physics

Title and abstract changed, manuscript shortened. Submitted to Nonlinearity, 8 pages

Scientific paper

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.

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