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To find the motion of a rectangular membrane with sides of length L_x and L_y (in the absence of gravity), use the two-dimensional wave 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 ...

The Ablowitz-Ramani-Segur conjecture states that a nonlinear partial differential equation is solvable by the inverse scattering method only if every nonlinear ordinary ...

The system of partial differential equations describing fluid flow in the absence of viscosity, given by (partialu)/(partialt)+u·del u=-(del P)/rho, where u is the fluid ...

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 ...

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 ...

Written in the notation of partial derivatives, the d'Alembertian square ^2 in a flat spacetime is defined by square ^2=del ^2-1/(c^2)(partial^2)/(partialt^2), where c is the ...

A singular point of an algebraic curve is a point where the curve has "nasty" behavior such as a cusp or a point of self-intersection (when the underlying field K is taken as ...

Delta_hf(x)=(f(x+h)-f(x))/h=(Deltaf)/h. It gives the slope of the secant line passing through f(x) and f(x+h). In the limit h->0, the difference quotient becomes the partial ...

A number of closed-form constants can be obtained for generalized continued fractions having particularly simple partial numerators and denominators. The Ramanujan continued ...