Quantcast
  • Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.

News

PO is now at the Physics Department of Bielefeld University!

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback

Attributions

(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,047 questions , 2,200 unanswered
5,345 answers , 22,709 comments
1,470 users with positive rep
816 active unimported users
More ...

  Recommendations relating integrability and Lax potentials

+ 5 like - 0 dislike
1624 views

I was wondering if anybody can recommend notes/books that discusses integrability (i.e. models that possess as many conserved quantities as its number of degrees of freedom)? I'm particular interested to better understand the Lax potential and understand the maths behind the so-called graded \(\mathrm{sl}(2)\) loop algebra.

asked Nov 13, 2014 in Resources and References by Hunter (520 points) [ no revision ]
recategorized Nov 13, 2014 by Jia Yiyang

I'm not sure if this touches what you're looking for, but on the topic of integrability, I recall reading Gleb Arutyunov's pedagogical notes ("students seminar"), available online at http://www.staff.science.uu.nl/~aruty101/teaching.htm

@Siva thanks for your answer. These notes certainly look interesting.

2 Answers

+ 4 like - 0 dislike

For integrable partial differential systems which are dispersionless a.k.a. hydrodynamic-type, i.e. can be written as quasilinear first-order homogeneous systems, in the case of two independent variables see e.g. these lecture notes, Section 3 of this article, and references therein; in the case of three independent variables see Section 3 of this same article,  subsubsection 10.3.3 of this book, and these lecture notes, and references therein; for the case of four independent variables see introductory part of this article, the same book as before, and references therein. The book in question in fact is a good introduction to integrable partial differential systems in general.

answered Sep 6, 2018 by a-user (40 points) [ revision history ]
edited Oct 16, 2018 by a-user
+ 3 like - 0 dislike

An excellent book on classical integrability, available online, is 

O Babelon, D Bernard, M Talon, Introduction to classical integrable systems, Cambridge University Press 2003.

answered Nov 17, 2014 by Arnold Neumaier (15,787 points) [ no revision ]
Thank you; this seems very useful!!

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
p$\varnothing$ysicsOverflow
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
Please complete the anti-spam verification




user contributions licensed under cc by-sa 3.0 with attribution required

Your rights
...