Toda lattice and Korteweg de Vries relation

  • Thread starter Thread starter Ludo_Z
  • Start date Start date
  • Tags Tags
    Lattice Relation
AI Thread Summary
The discussion focuses on the relationship between the Toda lattice and the Korteweg de Vries (KdV) equation, emphasizing the former as a finite-dimensional counterpart to the latter. A recommended resource is M. Toda's book "Theory of Nonlinear Lattices" from 1981, which provides valuable insights. Additionally, the initial identification of this relationship was made by Flaschka in 1974, with relevant details found in his article published in Physical Review B. These references are essential for understanding the connections between these two mathematical constructs. The Toda lattice and KdV equation are crucial in the study of integrable systems and nonlinear dynamics.
Ludo_Z
Messages
3
Reaction score
0
Does anybody know where I can find a good reference which describes in a simple way the relations between the Toda lattice and the Korteweg de Vries equation and in particular the former as the finite-dimensional equivalent of the latter?
 
Physics news on Phys.org
Relation of Toda and Kdv

A good place to start is the book by M. Toda
 
Thank you, the book "Theory of nonlinear lattices" (1981) has been indeed helpful.

I have also found out that the relationship was first pointed out by Flaschka in 1974 and should be described in on of his articles (Phys. Rev. B 9, 1924–1925 (1974), http://prola.aps.org/abstract/PRB/v9/i4/p1924_1).
 
Thread 'Question about pressure of a liquid'

Thread 'Question about pressure of a liquid'

I am looking at pressure in liquids and I am testing my idea. The vertical tube is 100m, the contraption is filled with water. The vertical tube is very thin(maybe 1mm^2 cross section). The area of the base is ~100m^2. Will he top half be launched in the air if suddenly it cracked?- assuming its light enough. I want to test my idea that if I had a thin long ruber tube that I lifted up, then the pressure at "red lines" will be high and that the $force = pressure * area$ would be massive...
View full post »

Thread 'Why is the 3 body problem unsolvable? And what will happen if someone solves it?'

I feel it should be solvable we just need to find a perfect pattern, and there will be a general pattern since the forces acting are based on a single function, so..... you can't actually say it is unsolvable right? Cause imaging 3 bodies actually existed somwhere in this universe then nature isn't gonna wait till we predict it! And yea I have checked in many places that tiny changes cause large changes so it becomes chaos........ but still I just can't accept that it is impossible to solve...
View full post »

Similar threads

B How does lattice vibration affect electron mobility in semiconductor?
Replies
1
Views
1K
Voltage and effective resistance of an infinite lattice of resistors
Replies
2
Views
2K
A "Monstrous Higgs and Leech Spacetime"
Replies
0
Views
3K
I Principle of relativity and Galileo's group
Replies
10
Views
2K
I Is the Continuum Limit of Spin Foam Dynamics Equivalent to Massless Gravitons?
Replies
2
Views
3K
A Confusion with finite temperature and lattice formulation
Replies
3
Views
2K
I Problems involving combinatorics of lattice with certain symmetries
Replies
2
Views
1K
I Bloch functions and momentum of electrons in a lattice
Replies
20
Views
7K
I Understanding Ultrasound Attenuation and Reflection in Aluminum Sheets
Replies
15
Views
2K
I Is nonlinear acoustics in mainstream physics?
Replies
42
Views
4K

Hot Threads

Recent Insights

Back
Top