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This book contains the introduction and preliminaries of Lie and Noether theory. The conservation laws of the (1 + n)-dimensional heat equation on curved surfaces and the derivation of conserved quantities of the (1 + 2)-dimensional wave equation on different surfaces is discussed in detail. This book deals with conserved quantities of the (1 + n)-dimensional heat equation. The effect of a background metric on the symmetries of the nonlinear (1 + 2)-dimensional heat equation is also presented here, then all possible reduced equations up to conjugacy classes of the time dependent…mehr

Produktbeschreibung
This book contains the introduction and preliminaries of Lie and Noether theory. The conservation laws of the (1 + n)-dimensional heat equation on curved surfaces and the derivation of conserved quantities of the (1 + 2)-dimensional wave equation on different surfaces is discussed in detail. This book deals with conserved quantities of the (1 + n)-dimensional heat equation. The effect of a background metric on the symmetries of the nonlinear (1 + 2)-dimensional heat equation is also presented here, then all possible reduced equations up to conjugacy classes of the time dependent Ginzburg-Landau model are calculated and then the (1 + 2)-dimensional heat equation on the torus is considered, subalgebras are classified up to conjugacy classes and finally some solutions are calculated. A complete group classification of the (1 + n)-dimensional Klein-Gordon equation and nonlinear (1 + 2)-dimensional wave equation on the sphere and torus is presented here.
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Autorenporträt
Assistant Professor of Mathematics at Qassim University, since 2012. He received M.Sc. from University of Engineering and Technology, Lahore ,Pakistan in 2004 and his Ph.D. in Applied Mathematics from Lahore University of Management Sciences, Lahore, Pakistan in 2011. His research interest is in Applied Mathematics, focusing on Mathematical Physics