Search Results for ""

Find the tunnel between two points A and B on a gravitating sphere which gives the shortest transit time under the force of gravity. Assume the sphere to be nonrotating, of ...

A Bäcklund transformation allows additional solutions to a nonlinear partial differential equations to be found if one particular solution is already known.

The Christoffel symbols are tensor-like objects derived from a Riemannian metric g. They are used to study the geometry of the metric and appear, for example, in the geodesic ...

The Einstein field equations are the 16 coupled hyperbolic-elliptic nonlinear partial differential equations that describe the gravitational effects produced by a given mass ...

The partial differential equation (1-u_t^2)u_(xx)+2u_xu_tu_(xt)-(1+u_x^2)u_(tt)=0.

The partial differential equation u_t=Du_(xx)+u-u^2.

The Rabinovich-Fabrikant equation is the set of coupled linear ordinary differential equations given by x^. = y(z-1+x^2)+gammax (1) y^. = x(3z+1-x^2)+gammay (2) z^. = ...

Fok (1946) and Hazewinkel (1988, p. 65) call v(z) = 1/2sqrt(pi)Ai(z) (1) w_1(z) = 2e^(ipi/6)v(omegaz) (2) w_2(z) = 2e^(-ipi/6)v(omega^(-1)z), (3) where Ai(z) is an Airy ...

The partial differential equation u_t+u_x+uu_x-u_(xxt)=0 (Benjamin et al. 1972; Arvin and Goldstein 1985; Zwillinger 1997, p. 130). A generalized version is given by u_t-del ...

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