All Questions
8 questions
6
votes
1
answer
663
views
Lax pair of an integrable non-linear PDE
The following is a fourth-order non-linear PDE that passes the Painleve integrability test
$$\left(1+x^{2}\right)^{2}u_{xxxx} + 8x\left(1+x^{2}\right)u_{xxx} + 4\left(1+3x^{2}\right)u_{xx}+ t\left(...
- 449
2
votes
1
answer
142
views
Two questions on Zuber's "KdV and W-flows"
I'm having difficulty following computations in the paper "KdV and W-flows" by Zuber.
On pg. 2, what would be the conserved quantity $I_4$, related to the conservation laws of the KdV hierarchy? (...
- 10.5k
8
votes
1
answer
359
views
Lax pairs in an abstract formalism
I am reading Integrals of Nonlinear Equations of
Evolution and Solitary Waves by Peter Lax and I'm having a hard time. The methods are pioneering, of course, but Lax does not bother much to provide ...
- 3,388
23
votes
4
answers
3k
views
What is an "integrable hierarchy"? (to a mathematician)
This is one of those "what is an $X$?" questions so let me apologize in advance.
By now I have already encountered the phrase "integrable hierarchy" in mathematical contexts (in particular the so ...
- 7,789
10
votes
2
answers
498
views
Proving a system is nonintegrable /not solvable with Inverse Scattering Transform
Question:
Given a PDE, is there a general method to show that it is not solvable using the inverse scattering transform?
Specifically, for the perturbed 1D NLS or the 2D cubic NLS, where was it ...
- 3,574
4
votes
2
answers
371
views
Literature on ZS-AKNS systems with independent potentials
For those with some familiarity with integrable systems, I'll summarize my question as such:
Where can I find literature on ZS-AKNS systems, and their solution via the inverse scattering transform, ...
- 319
9
votes
3
answers
3k
views
What is soliton
I am new to this word.. This is not research level problem and it is soft question in nature. Just for curiosity, i am asking..
In literature, i am finding following words:(Wikipedia+ others).
...
- 541
4
votes
0
answers
182
views
Uniqueness for solution of a d-dbar system related to Davey-Stewartson Solitons
This question concerns a system of equations that arise in the study of one-soliton solutions to the Davey-Stewartson equation.
In what follows, $f(z)$ denotes a function which depends smoothly (but ...
- 41