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dtau^2=-eta_(alphabeta)dxi^alphadxi^beta, or (d^2xi^alpha)/(dtau^2)=0.

A differential k-form is a tensor of tensor rank k that is antisymmetric under exchange of any pair of indices. The number of algebraically independent components in n ...

The twistor equation states that del _(A^')^((A)phi^(B...E))=0, where the parentheses denote symmetrization, in a Lorentz transformation, primed spinors transform under the ...

An equation involving a function f(x) and integrals of that function to solved for f(x). If the limits of the integral are fixed, an integral equation is called a Fredholm ...

The partial differential equation 1/(c^2)(partial^2psi)/(partialt^2)=(partial^2psi)/(partialx^2)-mu^2psi (1) that arises in mathematical physics. The quasilinear Klein-Gordon ...

The operator representing the computation of a derivative, D^~=d/(dx), (1) sometimes also called the Newton-Leibniz operator. The second derivative is then denoted D^~^2, the ...

The partial differential equation u_(xy)+(N(u_x+u_y))/(x+y)=0.

The partial differential equation (u_t)/(u_x)=1/4(u_(xxx))/(u_x)-3/8(u_(xx)^2)/(u_x^2)+3/2(p(u))/(u_x^2), where p(u)=1/4(4u^3-g_2u-g_3). The special cases ...

Differential Geometry

The van der Pol equation is an ordinary differential equation that can be derived from the Rayleigh differential equation by differentiating and setting y=y^'. It is an ...