Lie symmetries and their local determinacy for a class of differential-difference equations |
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| Institution: | 1. Department of Mathematics, Benha Faculty of Engineering, Benha University, Benha, Egypt;2. Department of Mathematics, Zhejiang Normal University, Jinhua 321004, Zhejiang, China;3. Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia;4. Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620, USA;5. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, Shandong, China;6. Department of Mathematical Sciences, International Institute for Symmetry Analysis and Mathematical Modelling, North-West University, Mafikeng Campus, Mmabatho 2735, South Africa |
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| Abstract: | Differential-difference equations (DDEs) un(k)(t) = Fn(t, un+a,…, un+b) for k ≥ 2 are studied for their differential Lie symmetries. We observe that while nonintrinsic Lie symmetries do exist in such DDEs, a great many admit only the intrinsic ones. We also propose a mechanism for automating symmetry calculations for fairly general DDEs, with a variety of features exemplified. In particular, the Fermi-Pasta-Ulam system is studied in detail and its new similarity solutions given explicitly. |
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