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Consider the following partial differential equation known as the Benjamin-Bona-Mahony BBM) equation: du at + + u = 0, where u(t, x) is the unknown

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Consider the following partial differential equation known as the Benjamin-Bona-Mahony BBM) equation: du at + + u = 0, where u(t, x) is the unknown function and (t, x) E R2. This equation is a model for uni-directional, small-amplitude water waves. Show that the solitary wave u(t, x) = sech? (4x - ;t) is a solution BBM equation. You may use, without proof, the following derivative formulae: d d -sech? (x) = -2 tanh(x)sech"(x), -tanh(x) = sech (x). dax d.x

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