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I need guidance regarding PDE.

If u have a nonlinear PDE as

Ut+Us+a*U*Us*b*Usss=0

where U is function of (s,t) and a,b are constants.

by introducing new variable x=s-t we will get

Ut+a*U*Ux+b*Uxxx=0

Ut means partial derivative w.r.t time

Us means partial derivative w.r.t s.

How can we get the second equation from the first one?

If u have a nonlinear PDE as

Ut+Us+a*U*Us*b*Usss=0

where U is function of (s,t) and a,b are constants.

by introducing new variable x=s-t we will get

Ut+a*U*Ux+b*Uxxx=0

Ut means partial derivative w.r.t time

Us means partial derivative w.r.t s.

How can we get the second equation from the first one?

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