Weak and Partial Symmetries of Nonlinear PDE in Two Independent Variables

DOI

10.2991/jnmp.1996.3.3-4.10How to use a DOI?

Abstract

Nonclassical infinitesimal weak symmetries introduced by Olver and Rosenau and partial symmetries introduced by the author are analyzed. For a family of nonlinear heat equations of the form ut = (k(u) ux)x + q(u), pairs of functions (k(u), q(u)) are pointed out such that the corresponding equations admit nontrivial two-dimensional modules of partial symmetries. These modules yield explicit solutions that look like u(t, x) = F((t) x + (t)) or u(t, x) = G(f(x) + g(t)).

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  - Evgenii M. Vorob'ev
PY  - 1996
DA  - 1996/09/02
TI  - Weak and Partial Symmetries of Nonlinear PDE in Two Independent Variables
JO  - Journal of Nonlinear Mathematical Physics
SP  - 330
EP  - 335
VL  - 3
IS  - 3-4
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.1996.3.3-4.10
DO  - 10.2991/jnmp.1996.3.3-4.10
ID  - Vorob'ev1996
ER  -