Journal of Nonlinear Mathematical Physics

Volume 3, Issue 1-2, May 1996, Pages 226 - 235

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

Authors
Z. JIANG
Corresponding Author
Z. JIANG
Available Online 19 December 2006.
DOI
https://doi.org/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.
Open Access
This is an open access article distributed under the CC BY-NC license.

Download article (PDF)

Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
3 - 1
Pages
226 - 235
Publication Date
2006/12
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.2991/jnmp.1996.3.1-2.27How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - JOUR
AU  - Z. JIANG
PY  - 2006
DA  - 2006/12
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  - https://doi.org/10.2991/jnmp.1996.3.1-2.27
ID  - JIANG2006
ER  -