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Let $u(t,x)$ be a function of the time $t$ and $x$ a real number. I define:

$$\partial_q u(t,x)=\frac{u(qt,x)-u(t,x)}{(q-1)t}$$

The q-KdV equation is:

$$\partial_q u =\partial_x^3 u + 6 u\partial_x u$$

Is the q-KdV equation an integrable system?

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