Pith. Sign in

RECORD

Group Classification of Generalised Eikonal Equations

PaperPDF from arXiv

data files

Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
X Bluesky LinkedIn Reddit Hacker News
Roman O. Popovych, Irina A. Yehorchenko (Institute of Mathematics, National Academy of Science of Ukraine)

Mathematical Physics · Submitted 22 Dec 2001

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim It allowed complete solution of the group classification problem for a class of equations for functions depending on multiple independent variables, where highest derivatives enter nonlinearly.

how it is stated · asserted 0.99 read the record →

Comment (0) Read on arXiv ↗
Cite ▾
arXiv IDmath-ph/0112055 (version 1)
Pith ID7VXGD62A, Pith's permanent record of this paper and its review
CitationIrina A. Yehorchenko (Institute of Mathematics, National Academy of Science of Ukraine), Roman O. Popovych. "Group Classification of Generalised Eikonal Equations." arXiv:math-ph/0112055 (2001). https://pith.science/paper/7VXGD62A
Claim paper

The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,829 input tokens.

What the abstract itself states, as probabilities: claims first 0.11 · states limitation 0.07 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.12 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

A new approach to the problem of group classification is applied to the class of first-order non-linear equations of the form $u_a u_a=F(t,u,u_t)$. It allowed complete solution of the group classification problem for a class of equations for functions depending on multiple independent variables, where highest derivatives enter nonlinearly. Equivalence groups of the class under consideration and algebraic properties of the symmetry algebra are studied. The class of equations considered presents generalisation of the eikonal and Hamilton-Jacobi equations. The paper contains the list of all non-equivalent equations from this class with symmetry extensions, and proofs of such non- equivalence. New first order non-linear equations possessing wide symmetry groups were constructed.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 A new approach to the problem of group classification is applied to the class of first-order non-linear equations of the form $u_a u_a=F(t,u,u_t)$. contribution 0.72 0.86 0.09 asserted 0.99
s1 It allowed complete solution of the group classification problem for a class of equations for functions depending on multiple independent variables, where highest derivatives enter nonlinearly. result 0.87 0.91 0.65 asserted 0.99
s2 Equivalence groups of the class under consideration and algebraic properties of the symmetry algebra are studied. contribution 0.96 0.90 0.09 asserted 0.97
s3 The class of equations considered presents generalisation of the eikonal and Hamilton-Jacobi equations. background 0.99 0.23 0.06 asserted 1.00
s4 The paper contains the list of all non-equivalent equations from this class with symmetry extensions, and proofs of such non- equivalence. result 0.61 0.94 0.28 asserted 1.00
s5 New first order non-linear equations possessing wide symmetry groups were constructed. result 0.73 0.95 0.22 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.77 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

A new approach to the problem of group classification is applied to the class of first-order non-linear equations of the form $u_a u_a=F(t,u,u_t)$. It allowed complete solution of the group classification problem for a class of equations for functions depending on multiple independent variables, where highest derivatives enter nonlinearly. Equivalence groups of the class under consideration and algebraic properties of the symmetry algebra are studied. The class of equations considered presents generalisation of the eikonal and Hamilton-Jacobi equations. The paper contains the list of all non-equivalent equations from this class with symmetry extensions, and proofs of such non- equivalence. New first order non-linear equations possessing wide symmetry groups were constructed.

Human review

How Pith checks papers → · Full audit of this paper →

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.