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title:
 
Direct Similarity Solution Method and Comparison with the Classical Lie Symmetry Solutions
publication:
 
JNMP
volume-issue:   3 - 1-2
pages:   226 - 235
ISSN:
   1402-9251
DOI:
   doi:10.2991/jnmp.1996.3.1-2.27 (how to use a DOI)
author(s):
 
Z. JIANG
publication date:
 
May 1996
abstract:
 
We study the general applicability of the Clarkson­Kruskal's direct method, which is known to be related to symmetry reduction methods, for the similarity solutions of nonlinear evolution equations (NEEs). We give a theorem that will, when satisfied, immediately simplify the reduction procedure or ansatz before performing any explicit reduction expansions. We shall apply the method to both scalar and vector NEEs in either 1+1 or 2+1 dimensions, including in particular, a variable coefficient KdV equation and the 2+1 dimensional Khokhlov­Zabolotskaya equation. Explicit solutions that are beyond the classical Lie symmetry method are obtained, with comparison discussed in this connection.
copyright:
  
© Atlantis Press. This article is distributed under the terms of the Creative Commons Attribution License, which permits non-commercial use, distribution and reproduction in any medium, provided the original work is properly cited.
full text:
 
3-1_2art27.pdf (175 K)