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The partial differential equation

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

The system of partial differential equations del ^2s-(|a|^2+1)s = 0 (1) del ^2a-del (del ·a)-s^2a = a. (2)

The partial differential equation u_t+2uu_x-nuu_(xx)+muu_(xxx)=0.

The partial differential equation P_t=P_(xx)-uP_x+partial/(partialx){[u-F(x)]P}.

The partial differential equation u_t=u_(xxxxx)+5/2u_(xxx)u+(25)/4u_(xx)u_x+5/4u^2u_x.

The partial differential equation u_t+del ^4u+del ^2u+1/2|del u|^2=0, where del ^2 is the Laplacian, del ^4 is the biharmonic operator, and del is the gradient.

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

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

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