References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt145",{id:"formSmash:upper:j_idt145",widgetVar:"widget_formSmash_upper_j_idt145",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt146_j_idt148",{id:"formSmash:upper:j_idt146:j_idt148",widgetVar:"widget_formSmash_upper_j_idt146_j_idt148",target:"formSmash:upper:j_idt146:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

Symmetries for a class of explicitly space- and time-dependent (1+1)-dimensional wave equationsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 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)
##### Abstract [en]

##### 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
##### Identifiers

URN: urn:nbn:se:ltu:diva-38089Local ID: c5b49920-9bfd-11db-8975-000ea68e967bISBN: 966-02-0343-8OAI: oai:DiVA.org:ltu-38089DiVA: diva2:1011588
##### Conference

International Conference Symmetry in Nonlinear Mathematical Physics : 07/07/1997 - 13/07/1997
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt375",{id:"formSmash:j_idt375",widgetVar:"widget_formSmash_j_idt375",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt381",{id:"formSmash:j_idt381",widgetVar:"widget_formSmash_j_idt381",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt387",{id:"formSmash:j_idt387",widgetVar:"widget_formSmash_j_idt387",multiple:true});
##### Note

Godkänd; 1997; 20061221 (kani)Available from: 2016-10-03 Created: 2016-10-03Bibliographically approved

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.

References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt1088",{id:"formSmash:lower:j_idt1088",widgetVar:"widget_formSmash_lower_j_idt1088",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt1089_j_idt1091",{id:"formSmash:lower:j_idt1089:j_idt1091",widgetVar:"widget_formSmash_lower_j_idt1089_j_idt1091",target:"formSmash:lower:j_idt1089:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});