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      Scaling, Self-similarity and Superposition

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          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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          Journal
          2009-08-24
          2010-01-18
          0908.3337

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

          Custom metadata
          Title and abstract changed, manuscript shortened. Submitted to Nonlinearity, 8 pages
          math-ph math.MP nlin.SI physics.flu-dyn

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