The partial differential equation 3/4 U_y + W_x = 0, where W_y + U_t - 1/4 U_(x x x) + 3/2 U U_x = 0 (Krichever and Novikov 1980; Novikov 1999). Zwillinger and Calogero and Degasperis give the equation as d/(dx)(u_t + u_(x x x) - 6u u_x) ± u_(y y) = 0. The modified Kadomtsev-Petviashvili equation is given by u_(x t) = u_(x x x) + 3u_(y y) - 6u_x^2 u_(x x) - 6u_y u_(x x) (Clarkson 1986; Zwillinger 1997, p. 133).

Kadomtsev-Petviashvili-Burgers equation | Korteweg-de Vries equation | Krichever-Novikov equation