Scaling, Self-similarity and Superposition

2009/08/24 by K. Y. Eksi, Eksi, K. Y.
Mathematics · Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Mathematical Physics (math-ph) #math-ph #math.MP #nlin.SI #physics.flu-dyn

paper · pdf · doi:10.48550/arxiv.0908.3337

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

arxiv created 2010/01/18 · arxiv updated 2010/02/08

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.

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