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The system of partial differential equations iu_t+u_(xx)+alphau_(yy)+betau|u|^2-uv=0 v_(xx)+gammav_(yy)+delta(|u|^2)_(yy)=0.

The system of partial differential equations u_t = (u^2-u_x+2v)_x (1) v_y = (2uv+v_x)_x. (2)

The system of partial differential equations u_t = 3ww_x (1) w_t = 2w_(xxx)+2uw_x+u_xw. (2)

The partial differential equation R[u](u_(rr)+(u_r)/r+u_(zz))=u_r^2+u_z^2, where R[u] is the real part of u (Calogero and Degasperis 1982, p. 62; Zwillinger 1997, p. 131).

The partial differential equation u_(xy)+(alphau_x-betau_y)/(x-y)=0.

The system of partial differential equations u_t = u_(xx)+u(u-a)(1-u)+w (1) w_t = epsilonu. (2)

The partial differential equation u_t=(1+ia)u_(xx)+(1+ic)u-(1+id)|u|^2u.

The partial differential equation u_t=u_(xxx)u^3.

The study, first developed by Boole, of shift-invariant operators which are polynomials in the differential operator D^~. Heaviside calculus can be used to solve any ordinary ...

The system of partial differential equations S_t=SxS_(xx).