All Questions
Tagged with integrable-systems mp.mathematical-physics
9 questions with no upvoted or accepted answers
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
3
votes
0
answers
264
views
KP tau-functions and $GL(\infty)$
It is usually assumed, that some version of the central extended $GL(\infty)$ group acts transitively on the space of tau-function of the KP integrable hierarchy. It means that any tau-function can be ...
- 1,343
3
votes
0
answers
153
views
Classical Yang-Baxter equation for Lie algebras and Lie superalgebras
The classical Yang-Baxter equation is
\begin{align}
[r_{12}, r_{13}] + [r_{12}, r_{23}] + [r_{13}, r_{23}] = 0. \quad (1)
\end{align}
What are the differences between this equation in the case of Lie ...
- 6,201
2
votes
0
answers
93
views
Representation theoretic definition of wavefunctions of an integrable hierarchy?
I am reading Kac's book on infinite dimensional lie algebras. In the last chapter, he starts with a highest weight module of an affine lie algebra $\mathfrak{g}(A)$, and uses it to define tau ...
user35360
2
votes
0
answers
165
views
Nature of separatrix in Fokker--Planck Hamiltonian with two degrees of freedom
Background The semiclassical (weak noise, small $D$) limit of the Fokker--Planck equation
$$\frac{\partial P}{\partial t}=D\frac{\partial^2 P}{\partial x^2}-\frac{\partial}{\partial x}(v(x) P)$$
can ...
- 1,038
1
vote
0
answers
71
views
Low-dimensional classical r-matrices
Let $g= gl_2$. Suppose that $r \in g \otimes g$ satisfies the following properties:
(1) $r_{12} + r_{21} \in g \otimes g$ is $g$-invariant, $r_{12} = r$, $r_{21} = \tau \ r_{12}$.
(2) $[r_{12}, r_{...
- 6,201
1
vote
0
answers
97
views
anomaly polynomial of generalized Hitchin system
I would like to ask about mathematical background of this object. So, I am trying to puzzle out with 4d $\mathcal{N}=2$ SQFT. As far as I can gather this theroy can be described in terms of ...
- 181
1
vote
0
answers
114
views
Divisors, factorisations of matrix valued functions, and the Lorentz group
How to construct a complex projective variety with several classes of non-intersecting divisors? How to keep the answer concrete and simple, so that explicit calculations can be done? And the problem -...
- 1,143
0
votes
0
answers
188
views
Do principally polarized abelian varieties enjoy a genus expansion?
This is a vague question from an interested outsider:
It is well known that abelian varieties which arise as Jacobian of a curve (or a bit more general as Prym variety) are distinguished by the fact ...
- 2,029