X-Nico

unusual facts about differential equation



Algebraic Riccati equation

The DARE arises in place of the CARE when studying discrete time systems; it is not obviously related to the differential equation studied by Riccati.

Ince equation

In mathematics, the Ince equation, named for Edward Lindsay Ince, is the differential equation

Ivan Vidav

Vidav got his Ph.D. under Plemelj's advisory in 1941 at the University of Ljubljana with a dissertation Kleinovi teoremi v teoriji linearnih diferencialnih enačb (Klein's theorems in the theory of linear differential equations).

Jean Trembley

Jean Trembley (1749 - September 18, 1811), born at Geneva, contributed to the development of differential equations, finite differences, and the calculus of probabilities.

Multiresolution analysis

It was introduced in this context in 1988/89 by Stephane Mallat and Yves Meyer and has predecessors in the microlocal analysis in the theory of differential equations (the ironing method) and the pyramid methods of image processing as introduced in 1981/83 by Peter J. Burt, Edward H. Adelson and James Crowley.

Singular solution

A singular solution ys(x) of an ordinary differential equation is a solution that is singular or one for which the initial value problem (also called the Cauchy problem by some authors) fails to have a unique solution at some point on the solution.


see also

Bessel function

This differential equation, and the Riccati–Bessel solutions, arises in the problem of scattering of electromagnetic waves by a sphere, known as Mie scattering after the first published solution by Mie (1908).

Calabi conjecture

Calabi transformed the Calabi conjecture into a non–linear partial differential equation of complex Monge–Ampere type, and showed that this equation has at most one solution, thus establishing the uniqueness of the required Kähler metric.

Eikonal

Eikonal equation, a non-linear partial differential equation encountered in problems of wave propagation.

Einstein–Brillouin–Keller method

for example, the work of Eric J. Heller and Emmanuel David Tannenbaum using a partial differential equation gradient descent approach.

Kaup

Kaup–Kupershmidt equation, the nonlinear fifth-order partial differential equation

Lewy's example

In the mathematical study of partial differential equations, Lewy's example is a celebrated example, due to Hans Lewy, of a linear partial differential equation with no solutions.

Liénard

Liénard equation, type of differential equation, after the French physicist Alfred-Marie Liénard

Painlevé

Painlevé transcendents/property, Ordinary differential equation solutions discovered by Paul Painlevé.

Riemann's differential equation

In mathematics, Riemann's differential equation, named after Bernhard Riemann, is a generalization of the hypergeometric differential equation, allowing the regular singular points to occur anywhere on the Riemann sphere, rather than merely at 0, 1, and ∞.

Vibrations of a circular membrane

Turning to the equation for R(r), with the observation that K=-\lambda^2, all solutions of this second-order differential equation are a linear combination of Bessel functions of order 0,

Vlasov equation

The Vlasov equation is a differential equation describing time evolution of the distribution function of plasma consisting of charged particles with long-range (for example, Coulomb) interaction.