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Consider the periodic nonlinear Schrödinger equation $$-i \partial_t u + \Delta u = f(|u|)u, \qquad u=u(t,x) \in \mathbb{C}, \; t\in \mathbb{R}, \; x\in \mathbb{T}^n,$$ where $\mathbb{T}:= \mathbb{R}/\...

I would like to ask a question that I had asked yesterday on the site math.stackexchange and I still have not received an answer. Suppose that we have a PDE that admit a solution $u$ that can be ...

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 ...

So, let's say we have a symplectic variety over $\mathbb{C}$, $M$, of dimension $2n$, and $f_1,\ldots,f_n$ Poisson commuting functions with $df_1\wedge\ldots\wedge df_n$ generically nonzero. Further ...