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 'Off resonance driving of a MW/RF cavity'

Hello! Let's say I have a cavity resonant at 10 GHz with a Q factor of 1000. Given the Lorentzian shape of the cavity, I can also drive the cavity at, say 100 MHz. Of course the response will be very very weak, but non-zero given that the Loretzian shape never really reaches zero. I am trying to understand how are the magnetic and electric field distributions of the field at 100 MHz relative to the ones at 10 GHz? In particular, if inside the cavity I have some structure, such as 2 plates...
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