Verifying Galilean Invariance of the KdV Equation

[squenshl]

Homework Statement

Show that the KdV has Galilean invariance.
That is u_t + 6uu_x + u_xxx = 0 is invariant under the transformation xi = x - ct, tau = t, psi = phi - c/6

Homework Equations

The Attempt at a Solution

Do we use the chain rule on these and plug into the KdV?

 

[HallsofIvy]

That would be what I would do. Essentially you just want to make that "change" of variables and show that you get exactly the same equation again. And changing variables in a differential equation involves the chain rule.

 

[squenshl]

Thanks.
So d/dx = xi_x*d/dxi + tau_x*d/dtau = d/dxi
and d/dt = xi_t*d/dxi + tau_t*d/dtau = -cd/dxi + d/dtau

 

[squenshl]

Got it.
Thanks.