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A precise definition of reduction of partial differential equations | | Renat Z. Zhdanov
; Ivan M. Tsyfra
; Roman O. Popovych
; | | Date: |
18 Jul 2002 | | Journal: | J. Math. Anal. Appl., 1999, V.238, 101-123 | | Subject: | Mathematical Physics; Analysis of PDEs; Exactly Solvable and Integrable Systems MSC-class: 35A30, 35L70, 58J70 | math-ph math.AP math.MP nlin.SI | | Abstract: | We give a comprehensive analysis of interrelations between the basic concepts of the modern theory of symmetry (classical and non-classical) reductions of partial differential equations. Using the introduced definition of reduction of differential equations we establish equivalence of the non-classical (conditional symmetry) and direct (Ansatz) approaches to reduction of partial differential equations. As an illustration we give an example of non-classical reduction of the nonlinear wave equation in (1+3) dimensions. The conditional symmetry approach when applied to the equation in question yields a number of non-Lie reductions which are far-reaching generalization of the well-known symmetry reductions of the nonlinear wave equations. | | Source: | arXiv, math-ph/0207023 | | Services: | Forum | Review | PDF | Favorites | |
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