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

Forskningsoutput: Tidskriftsbidrag › Artikel › Vetenskaplig › Peer review

Sammanfattning

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.

Originalspråk	Engelska
Artikelnummer	103322
Tidskrift	Results in Physics
Volym	19
DOI	https://doi.org/10.1016/j.rinp.2020.103322
Status	Publicerad - 2020
MoE-publikationstyp	A1 Tidskriftsartikel-refererad

Åtkomst av dokument

10.1016/j.rinp.2020.103322Licens: Ospecificerad

AlgoNano: Algorithmic Nanotechnology: Modeling, Design and Automation of Synthetic Self-Assembly Systems (AlgoNano) (Academy of Finland)
Czeizler, E.
01/09/17 → 31/08/21
Projekt: FA/Övriga Forskningsråd

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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.",

keywords = "Symmetries of PDE, Quasi-Miura algebraic methods, Inviscid Burgers equation",

author = "G. Barad and E. Czeizler and A. Paun",

year = "2020",

doi = "10.1016/j.rinp.2020.103322",

language = "English",

volume = "19",

journal = "Results in Physics",

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AU - Barad, G.

AU - Czeizler, E.

AU - Paun, A.

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Y1 - 2020

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

Sammanfattning

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Projekt

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

Citera det här