Questions tagged [integrable-systems]
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7 questions from the last 365 days
2
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Wobbly divisor in the moduli space of rank 2 degree 1semi-stable vector bundles over a curve of genus 2
I am looking at Nigel Hitchin's lecture "Higgs fields in low genus" on the occasion of Oscar Garcia-Prada's 60th birthday. In the rank 2 odd degree case, he mentions a map $f$ from the ...
2
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On reproducing the Poincare section figure in a paper by Sato, Akiyama and Doyne Farmer [closed]
I am trying to reproduce Figure 1 in the paper "Chaos in learning a simple two-person game" (English) Proc. Natl. Acad. Sci. USA 99, No. 7, 4748-4751 (2002) (MR1895748, Zbl 1015.91014), by ...
1
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KdV/KP-II equation with upper semicontinuous initial data and viscosity solutions
In the article "KP governs random growth off a 1-dimensional substrate", they study the KP-II equation: the function $\phi(t,x,r)=\partial_{r}^{2}\log(F)$ satisfies
$$\partial_{t}\phi+\frac{...
- 5,474
2
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A strange identity between generalized basic hypergeometric series
Calculating matrix elements in some quantum integrable system, I encountered a strange $q$-series identity for non-terminating basic hypergeometric functions $\phantom{i}_3\phi_2$. It comes from the ...
- 21
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A parabolic–hyperbolic in 3d: $\partial_t u(x,y,t)=\frac{1}{2}(\partial_{xx}u(x,y,t)-\partial_{yy}u(x,y,t))$
I was just wondering if somebody can provide some references for the parabolic–hyperbolic pde
$$\partial_t u(x,y,t)=\frac{1}{2}(\partial_{xx}u(x,y,t)-\partial_{yy}u(x,y,t)).$$
Apparently, the IVP ...
- 5,474
5
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1
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Weakly involutive $R$-matrices and representations of the symmetric group $S_N$ in restricted subspaces of $V^{\otimes N}$
An $R$-matrix is a matrix $R\in\operatorname{End}(V\otimes V)$ (where $V$ is a finite dimensional vector space) that solves the Yang–Baxter equation
$$R_{12}R_{23}R_{12}=R_{23}R_{12}R_{23},$$
where ...
- 727
2
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148
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Nilpotent polynomial matrices over $F_q$ - polynomial count variety ? ( Nilpotent cone for Hitchin-Gaudin like integrable system)
Context: Number of nilpotent $n\times n $ matrices over $F_q$ is $q^{n(n-1)}$ classical result due to Ph.Hall, M.Gerstenhaber (see very nice exposition by T.Leinster at n-cat-cafe/arxiv) which have ...
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