Question: Show that u(x, t) = sech 2 (x t) satisfies the KortewegdeVries equation (which arises in the study of water waves): 4u+ Uxxx +12uux

Show that u(x, t) = sech2(x − t) satisfies the Korteweg–deVries equation (which arises in the study of water waves):

4u+ uxxx +12uux = 0

4u+ Uxxx +12uux = 0

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