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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 Frobenius equation is the Diophantine equation a_1x_1+a_2x_2+...+a_nx_n=b, where the a_i are positive integers, b is an integer, and the solutions x_i are nonnegative ...

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 quantum electrodynamical law which applies to spin-1/2 particles and is the relativistic generalization of the Schrödinger equation. In 3+1 dimensions (three space ...

The Schrödinger equation describes the motion of particles in nonrelativistic quantum mechanics, and was first written down by Erwin Schrödinger. The time-dependent ...

A quartic equation is a fourth-order polynomial equation of the form z^4+a_3z^3+a_2z^2+a_1z+a_0=0. (1) While some authors (Beyer 1987b, p. 34) use the term "biquadratic ...

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

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 ...