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Structure of symmetry of PDE: exploiting partially integrated systems

Published: 28 July 2014 Publication History

Abstract

This work is part of a sequence in which we develop and refine algorithms for computer symmetry analysis of differential equations. We show how to exploit partially integrated forms of symmetry defining systems to assist the differential elimination algorithms that uncover structure of the Lie symmetry algebras. We thus incorporate a key advantage of heuristic integration methods, that of exploiting easy integrals of simple (e.g. one term) PDE that frequently occur in such analyses. A single unified method is given that computes structure constants whether the defining system is unsolved, or has been partially or completely integrated.
We also give a symbolic-numeric algorithm which for the first time can determine the structure of Lie symmetry algebras specified by defining systems that contain floating point coefficients. This algorithm incorporates a numerical version of the Cartan-Kuranishi prolongation projection algorithm from the geometry of differential equations.

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Cited By

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  • (2023)Symbolic and numeric computation of symmetries for a class of Schrödinger Equations2023 25th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)10.1109/SYNASC61333.2023.00016(68-75)Online publication date: 11-Sep-2023
  • (2022)Algorithm for intersecting symbolic and approximate linear differential varieties2022 24th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)10.1109/SYNASC57785.2022.00020(63-70)Online publication date: Sep-2022
  • (2019)Introduction of the MapDE Algorithm for Determination of Mappings Relating Differential EquationsProceedings of the 2019 International Symposium on Symbolic and Algebraic Computation10.1145/3326229.3326259(331-338)Online publication date: 8-Jul-2019
  • Show More Cited By

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cover image ACM Other conferences
SNC '14: Proceedings of the 2014 Symposium on Symbolic-Numeric Computation
July 2014
154 pages
ISBN:9781450329637
DOI:10.1145/2631948
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Sponsors

  • 973 Program: National Basic Research Program of China
  • KLMM: Key Laboratory of Mathematics Mechanization
  • MapleSoft
  • ORCCA: Ontario Research Centre for Computer Algebra
  • NSFC: Natural Science Foundation of China
  • Chinese Academy of Engineering: Chinese Academy of Engineering
  • NAG: Numerical Algorithms Group

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 28 July 2014

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Author Tags

  1. Lie algebra
  2. algorithm
  3. defining equations
  4. differential algebra
  5. differential elimination
  6. involutivity
  7. numerical
  8. structure constants
  9. symmetry

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  • Research-article

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SNC '14
Sponsor:
  • 973 Program
  • KLMM
  • ORCCA
  • NSFC
  • Chinese Academy of Engineering
  • NAG
SNC '14: Symbolic-Numeric Computation 2014
July 28 - 31, 2014
Shanghai, China

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Cited By

View all
  • (2023)Symbolic and numeric computation of symmetries for a class of Schrödinger Equations2023 25th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)10.1109/SYNASC61333.2023.00016(68-75)Online publication date: 11-Sep-2023
  • (2022)Algorithm for intersecting symbolic and approximate linear differential varieties2022 24th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)10.1109/SYNASC57785.2022.00020(63-70)Online publication date: Sep-2022
  • (2019)Introduction of the MapDE Algorithm for Determination of Mappings Relating Differential EquationsProceedings of the 2019 International Symposium on Symbolic and Algebraic Computation10.1145/3326229.3326259(331-338)Online publication date: 8-Jul-2019
  • (2017)Algorithmic calculus for Lie determining systemsJournal of Symbolic Computation10.1016/j.jsc.2016.03.00279:P2(482-498)Online publication date: 1-Mar-2017

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