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

The partial differential equation u_t=del ·(u^mdel u).

The partial differential equation u_t+45u^2u_x+15u_xu_(xx)+15uu_(xxx)+u_(xxxxx)=0.

The partial differential equation u_(xt)=sinhu, which contains u_(xt) instead of u_(xx)-u_(tt) and sinhu instead to sinu, as in the sine-Gordon equation (Grauel 1985; ...

The partial differential equation del ^2u+lambda^2sinhu=0, where del ^2 is the Laplacian (Ting et al. 1987; Zwillinger 1997, p. 135).

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

The partial differential equation u_(yy)=yu_(xx).