Lie and Noether point symmetries of a class of quasilinear systems of second-order differential equations

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• 作者：Andronikos Paliathanasis^a ; ^{anpaliat@phys.uoa.gr" class="auth_mail" title="E-mail the corresponding author} ; Michael Tsamparlis^b ; ^{mtsampa@phys.uoa.gr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Lie symmetries ; Noether symmetries ; Quasilinear systems
• 刊名：Journal of Geometry and Physics
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：107
• 期：Complete
• 页码：45-59
• 全文大小：533 K

文摘

We study the Lie and Noether point symmetries of a class of systems of second-order differential equations with n$n$ independent and 322e2fc4b12363e27cb7143ed313" title="Click to view the MathML source">m$m$ dependent variables (n×m$n\times m$ systems). We solve the symmetry conditions in a geometric way and determine the general form of the symmetry vector and of the Noetherian conservation laws. We prove that the point symmetries are generated by the collineations of two (pseudo)metrics, which are defined in the spaces of independent and dependent variables. We demonstrate the general results in two special cases (a) a system of 322e2fc4b12363e27cb7143ed313" title="Click to view the MathML source">m$m$ coupled Laplace equations and (b) the Klein–Gordon equation of a particle in the context of Generalized Uncertainty Principle. In the second case we determine the complete invariant group of point transformations, and we apply the Lie invariants in order to find invariant solutions of the wave function for a spin-0 particle in the two dimensional hyperbolic space.