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The system of partial differential equations U_t=U·U_(xx)+U·LambdaU.

The partial differential equation u_(tt)-u_(xx)-u+u^3=0.

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

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

The Benney equation in 1+1 dimensions is the nonlinear partial differential equation ...

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

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

In two-dimensional Cartesian coordinates, attempt separation of variables by writing F(x,y)=X(x)Y(y), (1) then the Helmholtz differential equation becomes ...

The system of partial differential equations f_x = 2fgc(x-t) (1) g_t = 2fgc(x-t). (2)

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.