Talk:Linear stability

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This paragraph doesn't make sense:

In mathematics, in the theory of differential equations and dynamical systems, a particular stationary or quasistationary solution to a nonlinear system is called linearly or exponentially unstable if the linearization of the equation at this solution has the form drdt=Ar, where A is a linear operator whose spectrum contains points with positive real part. If there are no such eigenvalues, the solution is called linearly, or spectrally, stable.

Which "such" eigenvalues? I'm going to guess a coherent explanation, but it would be nice if a domain expert checked it.

--Livingthingdan (talk) 18:14, 27 July 2014 (UTC)Reply

I am struggling to reproduce ex2. Three issues are:

(1) In the NLS

${\displaystyle i{\frac {\partial u}{\partial t}}=-{\frac {\partial ^{2}u}{\partial x^{2}}}-|u|^{2k}u}$,

should ${\displaystyle k}$ be in the exponential? Seems like it should be a coefficient.

(2) Is ${\displaystyle \phi }$ real?

(3) Should ${\displaystyle L_{1}}$ have a term ${\displaystyle k(2+1)}$, not ${\displaystyle (2k+1)}$?

206.87.216.116 (talk) 20:54, 31 July 2019 (UTC)Reply