Inner symmetries of the spatially singular part of the solutions of the Burgers equation and their Lie representations

G. Barad; E. Czeizler; A. Paun

doi:10.1016/j.rinp.2020.103322

Inner symmetries of the spatially singular part of the solutions of the Burgers equation and their Lie representations

G. Barad, E. Czeizler, A. Paun

Research output: Contribution to journal › Article › Scientific › peer-review

Abstract

We describe two new discrete symmetries of the inviscid Burgers (or Riemann-Hopf) equation ut+uux=0. We derived both of them using a local, formal approach of Hopf algebraic renormalization, a tool recently used in algorithmic computations. We prove that one of them is a Lie point transformation. Symmetries generate new exact solutions from the known solutions and provide useful frames of reference in the study of shock wave formation.

Original language	English
Article number	103322
Journal	Results in Physics
Volume	19
DOIs	https://doi.org/10.1016/j.rinp.2020.103322
Publication status	Published - 2020
MoE publication type	A1 Journal article-refereed

Keywords

Symmetries of PDE
Quasi-Miura algebraic methods
Inviscid Burgers equation

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10.1016/j.rinp.2020.103322Licence: Unknown

AlgoNano: Algorithmic Nanotechnology: Modeling, Design and Automation of Synthetic Self-Assembly Systems (AlgoNano) (Academy of Finland)
Czeizler, E. (Principal Investigator)
01/09/17 → 31/08/21
Project: Research Council of Finland/Other Research Councils

Cite this

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title = "Inner symmetries of the spatially singular part of the solutions of the Burgers equation and their Lie representations",

abstract = "We describe two new discrete symmetries of the inviscid Burgers (or Riemann-Hopf) equation ut+uux=0. We derived both of them using a local, formal approach of Hopf algebraic renormalization, a tool recently used in algorithmic computations. We prove that one of them is a Lie point transformation. Symmetries generate new exact solutions from the known solutions and provide useful frames of reference in the study of shock wave formation.",

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AU - Barad, G.

AU - Czeizler, E.

AU - Paun, A.

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N2 - We describe two new discrete symmetries of the inviscid Burgers (or Riemann-Hopf) equation ut+uux=0. We derived both of them using a local, formal approach of Hopf algebraic renormalization, a tool recently used in algorithmic computations. We prove that one of them is a Lie point transformation. Symmetries generate new exact solutions from the known solutions and provide useful frames of reference in the study of shock wave formation.

AB - We describe two new discrete symmetries of the inviscid Burgers (or Riemann-Hopf) equation ut+uux=0. We derived both of them using a local, formal approach of Hopf algebraic renormalization, a tool recently used in algorithmic computations. We prove that one of them is a Lie point transformation. Symmetries generate new exact solutions from the known solutions and provide useful frames of reference in the study of shock wave formation.

KW - Symmetries of PDE

KW - Quasi-Miura algebraic methods

KW - Inviscid Burgers equation

U2 - 10.1016/j.rinp.2020.103322

DO - 10.1016/j.rinp.2020.103322

M3 - Article

SN - 2211-3797

VL - 19

JO - Results in Physics

JF - Results in Physics

M1 - 103322

ER -

Inner symmetries of the spatially singular part of the solutions of the Burgers equation and their Lie representations

Abstract

Keywords

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Projects

AlgoNano: Algorithmic Nanotechnology: Modeling, Design and Automation of Synthetic Self-Assembly Systems (AlgoNano) (Academy of Finland)

Cite this