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Results tagged with reference-request
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user 106467
This tag is used if a reference is needed in a paper or textbook on a specific result.
4
votes
References for existence of solutions to overdetermined system of partial differential inequ...
Existence theorems for real analytic pde systems were developed by Riquier and Janet in the first quarter of the twentieth century (see, for example, Riquier's 1910 book Les systèmes d'équations aux d …
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0
votes
Non-integrability of Abel's equation
The paper by Primitivo B. Acosta-Humánez, J. Tomás Lázaro, Juan J. Morales-Ruiz and Chara Pantazi Differential Galois theory and non-integrability of plane polynomial vector fields, J. Differential Eq …
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6
votes
Application of Lie group analysis of PDE (beyond calculation of exact solutions)
The book by Olle Stormark, Lie's Structural Approach to PDE Systems, Cambridge 2000 provides an introduction to a number of topics on the relationship between Lie groups and characteristics of PDEs, i …
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8
votes
Accepted
Reference to formal approach to homotopy analysis method
The paper by Shijun Liao "Notes on the homotopy analysis method: Some definitions and theorems" Communications in Nonlinear Science and Numerical Simulation, 14(4) 2009 pp. 983-997 may be what you're …
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2
votes
References for infinite-dimensional integrable systems?
It's not entirely clear what you mean by a "physical/geometric understanding of the corresponding integrable system" because each one will be unique in some sense.
A good collection of survey papers …
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5
votes
Accepted
What would be a good introductory reference for learning jet-bundle theory?
Two articles by A.M. Vinogradov provide a gentle introduction:
"Local symmetries and conservation laws", Acta Applicandae Mathematica volume 2, pages 21–78(1984)
"An informal introduction to the geome …
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2
votes
Accepted
Egyptian number theory
According to the chapter on Egyptian mathematics and astronomy in the book by O. Neugebauer, The Exact Sciences in Antiquity (1951, 1957), Egyptian mathematics only involved basic arithmetic with posi …
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1
vote
Essays and thoughts on mathematics
A Mathematician's Miscellany (reprinted, with additional material, as
Littlewood's Miscellany by CUP in 1986) is worthwhile reading.
Clifford Truesdell published a series of essays as An Idiot's Fugi …
1
vote
Name of a Frobenius-like method for ODEs
Have you tried W. Wasow, Asymptotic Expansions for Ordinary Differential Equations (Wiley, 1965, Dover reprint 2018)?
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4
votes
Accepted
How did the term "space" in mathematics started to be understood as a set with a structure?
The web page http://www.map.mpim-bonn.mpg.de/Axiomatization_of_the_manifold_concept attributes the earliest definition to M. Fréchet (per user234212323's comment) and to F. Riesz.
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8
votes
English translation of Wilhelm Killing's 1889 paper
This paper has been translated by David Delphenich under the title of "The composition of continuous, finite, transformation groups" (see here).
[Note that the paper's date is given as 1869 in the tra …
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1
vote
Accepted
N-soliton, The Lax operator and the transmission coefficient
A good starting point for Lax pairs and how to find them is:
Mark Hickman, Willy Heremann, Jennifer Larue and Ünal Göktaş "Scaling invariant Lax pairs of nonlinear evolution equations" Applicable Anal …
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1
vote
Critical gKdV - tutorial
How about this lecture by Yvan Martel - https://www.youtube.com/watch?v=7ynK-udMZh0?
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6
votes
Autobiographies of mathematicians
Yvonne Choquet-Bruhat, A Lady Mathematician in This Strange Universe: Memoirs, author's translation of the French original, Une Mathematicienne dans cet étrange universe.
I think this review sums it u …
0
votes
Accepted
References for group of invariance of the Painlevé property
I assume "the book of Robert Conte" refers to The Painlevé Handbook by Robert Conte and Micheline Musette (Springer, 2008); the "groups of invariance of the Painlevé property" are briefly described in …
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