Volume 3, Issue 1-2, May 1996, Pages 226 - 235
Direct Similarity Solution Method and Comparison with the Classical Lie Symmetry Solutions
Available Online 1 May 1996.
- https://doi.org/10.2991/jnmp.1996.3.1-2.27How to use a DOI?
- 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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Cite this article
TY - JOUR AU - Z. JIANG PY - 1996 DA - 1996/05 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 - JIANG1996 ER -