Symmetry solutions of some nonlinear PDE's

(2005) Symmetry solutions of some nonlinear PDE's. Masters thesis, King Fahd University of Petroleum and Minerals.


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English Abstract

Finding solutions of nonlinear partial differential equations, either exact or analytical, is one of the challenging problems in applied mathematics. In particular, the case of higher-order systems of nonlinear partial differential equations poses the most difficult challenge. Lie symmetry method provides a powerful tool for the generation of transformations that can be used to transform the given differential equation to a simpler equation while preserving the invariance of the original equation. Consequently, it enjoys a widespread application and has attracted the attention of many researchers. In this research work a complete classification of a family of nonlinear (1+2)- dimensional wave equations, in which the nonlinearity is introduced through a function representing the wave speed, has been done. All possible symmetries of this wave equation are derived and a set of reductions to ordinary differential equations under two-dimensional sub-algebras is given.

Item Type: Thesis (Masters)
Subjects: Math
Department: College of Computing and Mathematics > Mathematics
Committee Advisor: Bokhari, A. H.
Committee Members: Zaman, Fiazuddin and Furati, Khaled M. and Messaoudi, Salim and Boucherif, Abdulkader
Depositing User: Mr. Admin Admin
Date Deposited: 22 Jun 2008 13:46
Last Modified: 01 Nov 2019 13:49