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Calculating Symmetries and Invariant Solutions of a Several Kinds of Evolution Equations by Wu’s Method

Author: SuDaoBiLiGe
Tutor: ChaoLu
School: Inner Mongolia University of Technology
Course: Computational Mathematics
Keywords: Wu's method Characteristic Set Partial differential equations ( group ) Potential Symmetries Invariant Solutions
CLC: O241.82
Type: Master's thesis
Year: 2005
Downloads: 56
Quote: 1
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Abstract


In this paper, using the differential form Wu's method calculation to determine the BBM-Burgers, Benjanmin Ono, NTE three potential symmetries of evolution equations and symmetry group invariant solutions . Symmetric generating function satisfied with Wu's method for determining the equations feature set of columns , then by the characteristics of the column set l column ( triangulation ) structure and the original to determine the relationship of the solution set of equations , solving the characteristic set of columns the corresponding equations, thereby determining the corresponding symmetric . This process simplifies the computational difficulties of determining equations overdetermined . 2 . Calculation to determine the classical symmetry of the three types of equations , solving its corresponding invariant solutions . 3 calculations to determine the three types of equations is determined by the primary and secondary conservation form potential symmetry, and were compared with classical symmetric . Function satisfies the equation under certain conditions , get rich potential symmetry ( symmetric) , provides the possibility of solving wider invariant solutions . 4 different symmetry in an invariant solutions of different times to produce a series of the exact solution of the three types of equations . This result is a new way to get the PDEs the exact solution given . 5 given the symmetry of the switching table , showing the relationship between the resulting symmetric algebraic . 6 gives some potential symmetry transformation group .

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CLC: > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Numerical Analysis > The numerical solution of differential equations, integral equations > Numerical Solution of Partial Differential Equations
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