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

The partial differential equation ((partial^2)/(partialt^2)-(partial^2)/(partialx^2))((u_(xy))/u)+2(u^2)_(xt)=0.

A second-order linear Hermitian operator is an operator L^~ that satisfies int_a^bv^_L^~udx=int_a^buL^~v^_dx. (1) where z^_ denotes a complex conjugate. As shown in ...

If all the eigenvalues of a real matrix A have real parts, then to an arbitrary negative definite quadratic form (x,Wx) with x=x(t) there corresponds a positive definite ...

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 Laplace transform is an integral transform perhaps second only to the Fourier transform in its utility in solving physical problems. The Laplace transform is particularly ...

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.

The general equation of fluid flow (lambda+2mu)del (del ·u)-mudel x(del xu)=rho(partial^2u)/(partialt^2), where mu and lambda are coefficients of viscosity, u is the velocity ...

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

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