Direct Similarity Solution Method and Comparison with the Classical Lie Symmetry Solutions

DOI

10.2991/jnmp.1996.3.1-2.27How to use a DOI?

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

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Z. Jiang
PY  - 1996
DA  - 1996/05/01
TI  - Direct Similarity Solution Method and Comparison with the Classical Lie Symmetry Solutions
JO  - Journal of Nonlinear Mathematical Physics
SP  - 226
EP  - 235
VL  - 3
IS  - 1-2
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.1996.3.1-2.27
DO  - 10.2991/jnmp.1996.3.1-2.27
ID  - Jiang1996
ER  -