2
$\begingroup$

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?

1 Answers 1

5

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