How to find Lie symmetries Symmetry Methods for Differential and Difference Equations?
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Lie symmetry analysis is a powerful tool for solving and reducing the order and nonlinearity of differential equations. It is widely used in various branches of science, including physics and chemistry. The method involves finding symmetries of the equations, computing transformed equivalent equations, and determining invariant solutions. Several papers have focused on applying Lie symmetry analysis to different types of equations, such as the generalized Zoomeron equations , KS-type equations , and the N-dimensional fractional heat equation . The results show that the number of symmetries and Lie brackets can be significantly reduced in the case of fractional order equations compared to integer order equations. The Lie algebras obtained through computation of Lie brackets and inspection of symmetries are found to be similar in some cases. Additionally, similarity solutions and reduction forms of the equations are derived using the Lie symmetry analysis .
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| The paper does not provide information on how to find Lie symmetries for differential and difference equations. The paper focuses on the Lie symmetry classification for the 1+1 and 1+2 generalized Zoomeron equations. | |
16 May 2023 | The paper does not provide information on how to find Lie symmetries for differential and difference equations. The paper focuses on the Lie symmetry classification for the 1+1 and 1+2 generalized Zoomeron equations. |
| The provided paper discusses the use of Lie symmetry analysis to find symmetries of general classes of the Kuramoto-Sivashinsky equation. It does not provide information on how to find Lie symmetries for differential and difference equations in general. |
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