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A partial differential equation which appears in differential geometry and relativistic field theory. Its name is a wordplay on its similar form to the Klein-Gordon equation. ...

The wave equation is the important partial differential equation del ^2psi=1/(v^2)(partial^2psi)/(partialt^2) (1) that describes propagation of waves with speed v. The form ...

An equation of the form P(x)=0, where P(x) is a polynomial.

A second-order partial differential equation arising in physics, del ^2psi=-4pirho. If rho=0, it reduces to Laplace's equation. It is also related to the Helmholtz ...

The partial differential equation w_t-6(w+epsilon^2w^2)w_x+w_(xxx)=0, which can also be rewritten (w)_t+(-3w^2-2epsilon^2w^3+w_(xx))_x=0.

An natural equation which expresses a curve in terms of its arc length s and tangential angle phi.

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

The differential equation obtained by applying the biharmonic operator and setting to zero: del ^4phi=0. (1) In Cartesian coordinates, the biharmonic equation is del ^4phi = ...

The linear Boussinesq equation is the partial differential equation u_(tt)-alpha^2u_(xx)=beta^2u_(xxtt) (1) (Whitham 1974, p. 9; Zwillinger 1997, p. 129). The nonlinear ...

An Cesàro equation is a natural equation which expresses a curve in terms of its arc length function s(t) and radius of curvature rho(t) (or equivalently, the curvature ...