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The partial differential equation 2u_(tx)+u_xu_(xx)-u_(yy)=0.

The partial differential equation (Cole and Cook 1986, p. 34; Zwillinger 1997, p. 134).

The system of partial differential equations U_t = [V,W] (1) V_t = [W,U] (2) W_t = [U,V], (3) where [A,B] denotes the commutator.

Partial differential equation boundary conditions which give the normal derivative on a surface.

The partial differential equation u_(xx)=au_(tt)+bu_t+cu.

The partial differential equation u_(xy)+alphau_x+betau_y+gammau_xu_y=0.

The partial differential equation iu_t+[(1+|u|^2u)^(-1/2)u]_(xx)=0.

The partial differential equation partial/(partialx)(u_t+uu_x+1/2u_(xxx)+u/(2t))+(3alpha^2)/(2t^2)u_(yy)=0 which arises in the study of water waves.

For the hyperbolic partial differential equation u_(xy) = F(x,y,u,p,q) (1) p = u_x (2) q = u_y (3) on a domain Omega, Goursat's problem asks to find a solution u(x,y) of (3) ...

Suppose <= is a partial ordering on a nonempty set A. Then the elements a,b in A are said to be comparable provided a<=b or b<=a. Because two elements in a partially ordered ...