Symmetries for a class of explicitly space- and time-dependent (1+1)-dimensional wave equations
1997 (English)In: Proceedings of the second international conference: Memorial Prof. W. Fushchych conference, July 7 - 13, 1997, Kyiv, Ukraine / [ed] Mykola Shkil, Kyev: Institute of Mathematics of the National Academy of Sciences of Ukraine , 1997, Vol. 1, 70-78 p.Conference paper (Refereed)
In this paper the nonlinear wave equation $\partial^2 u/\partial x_0^2-\partial^2 u/\partial x_1^2+f(x_0,x_1,u)=0$, where $f$ is an arbitrary smooth function of its arguments, is considered from the symmetry standpoint. The form of the most general Lie point symmetry generator of this equation is obtained. The classes of functions $f$, for which the equation in question admits a one-parameter Lie point symmetry group, are constructed. Then, the authors investigate the possible form of generators of conformal transformations, assuming the usual form of generators of Lorentz and scaling transformations, and study the wave equations invariant under such operators. The symmetry groups of obtained equations are used for the construction of ansätze and reductions of these equations to ordinary differential equations. $Q$-conditional (nonclassical) symmetries of the wave equation are also considered. Namely, the determining equations for the coefficients of a $Q$-conditional symmetry operator are found and their compatibility is investigated.
Place, publisher, year, edition, pages
Kyev: Institute of Mathematics of the National Academy of Sciences of Ukraine , 1997. Vol. 1, 70-78 p.
Research subject Mathematics
IdentifiersURN: urn:nbn:se:ltu:diva-38089Local ID: c5b49920-9bfd-11db-8975-000ea68e967bISBN: 966-02-0343-8OAI: oai:DiVA.org:ltu-38089DiVA: diva2:1011588
International Conference Symmetry in Nonlinear Mathematical Physics : 07/07/1997 - 13/07/1997
Godkänd; 1997; 20061221 (kani)2016-10-032016-10-03Bibliographically approved