# Two expressions of KdV Equation

I have seen two expressions of KdV Equation:

$$u_t-6uu_x+u_{xxx}=0$$ $$u_t+uu_x+u_{xxx}=0$$

Are they the same? How can I transform one from another?

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## 1 Answer

If $v = -6 u$, then $v_t + v v_x + v_{x x x} = -6 (u_t - 6 u u_x + u_{xxx})$.

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