This equation is connected to the "modified" version of this equation via the Miura transform. While this equation possesses an infinite number of conservation laws, a related equation proposed by Benjamin, Bona, and Mahony o
This equation is connected to the "modified" version of this equation via the Miura transform. While this equation possesses an infinite number of conservation laws, a related equation proposed by Benjamin, Bona, and Mahony only possesses three. This equation is integrable via the inverse scattering transform for the 1-dimensional Schrodinger equation. A 2+1 dimensional analogue of this equation is the Kadomtsev-Petviashvili equation. For a function f of one spatial dimension and time, this equation sets f-sub-t plus alpha f times f-sub-x plus f-sub-x-x-x to zero. A hyperbolic-secant-squared solution to this equation is one of the first discovered examples of soliton behavior. For 10 points, name this doubly eponymous nonlinear PDE used to model shallow water waves.