title: |
Direct Similarity Solution Method and Comparison with the Classical Lie Symmetry Solutions |
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publication: |
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| 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 |
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publication date: |
May 1996 |
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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. |
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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. |
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full text: |