Scaling, Self-similarity and Superposition
Mathematical Physics
2010-01-18 v2 math.MP
Exactly Solvable and Integrable Systems
Fluid Dynamics
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.
Cite
@article{arxiv.0908.3337,
title = {Scaling, Self-similarity and Superposition},
author = {K. Y. Eksi},
journal= {arXiv preprint arXiv:0908.3337},
year = {2010}
}
Comments
Title and abstract changed, manuscript shortened. Submitted to Nonlinearity, 8 pages