Dispersive partial differential equation

In mathematics, a dispersive partial differential equation or dispersive PDE is a partial differential equation that is dispersive. In this context, dispersion means that waves of different wavelength propagate at different phase velocities.

Examples

Linear equations

• Euler–Bernoulli beam equation with time-dependent loading
• Airy equation
• Schrödinger equation
• Klein–Gordon equation

Nonlinear equations

• nonlinear Schrödinger equation
• Korteweg–de Vries equation (or KdV equation)
• Boussinesq equation (water waves)
• sine–Gordon equation

See also

• Dispersion (optics)
• Dispersion (water waves)

External links

• The Dispersive PDE Wiki.

This mathematical analysis–related article is a stub. You can help Wikipedia by expanding it.v · Categories: Mathematical analysis stubs Partial differential equations Non-linear systems Wikimedia Foundation. 2010. Игры ⚽ Поможем написать реферат God's Gonna Cut You Down Pribytki Look at other dictionaries: Partial differential equation — A visualisation of a solution to the heat equation on a two dimensional plane In mathematics, partial differential equations (PDE) are a type of differential equation, i.e., a relation involving an unknown function (or functions) of several… …   Wikipedia List of nonlinear partial differential equations — In mathematics and physics, nonlinear partial differential equations are (as their name suggests) partial differential equations with nonlinear terms. They describe many different physical systems, ranging from gravitation to fluid dynamics, and… …   Wikipedia Dispersive — partial differential equation Dispersive phase from Biological dispersal Dispersive medium dispersive line dispersive mass transfer dispersive power dispersive fading This disambiguation page lists articles associated with the same title. If an …   Wikipedia Korteweg–de Vries equation — In mathematics, the Korteweg–de Vries equation (KdV equation for short) is a mathematical model of waves on shallow water surfaces. It is particularly notable as the prototypical example of an exactly solvable model, that is, a non linear partial …   Wikipedia Dispersionless equation — Dispersionless (or quasi classical) limits of integrable partial differential equations (PDE) arise in various problems of mathematics and physics and are intensively studied in the recent literature (see, f.i., [1] [5]). Contents 1 Examples 1.1… …   Wikipedia Wave equation — Not to be confused with Wave function. The wave equation is an important second order linear partial differential equation for the description of waves – as they occur in physics – such as sound waves, light waves and water waves. It arises in… …   Wikipedia Electromagnetic wave equation — The electromagnetic wave equation is a second order partial differential equation that describes the propagation of electromagnetic waves through a medium or in a vacuum. The homogeneous form of the equation, written in terms of either the… …   Wikipedia Schrödinger equation — For a more general introduction to the topic, please see Introduction to quantum mechanics. Quantum mechanics …   Wikipedia Nonlinear Schrödinger equation — This page is about the equation iψt = −½ψxx + κ|ψ|2ψ. For the equation iψt = −½ψxx + V(x)ψ + κ|ψ|2ψ, used in Bose–Einstein condensate theory, see Gross–Pitaevskii equation. In theoretical physics, the nonlinear Schrödinger equation (NLS) is a… …   Wikipedia Ishimori equation — The Ishimori equation (IE) is a partial differential equation proposed by the Japanese mathematician harvtxt|Y. Ishimori|1984. Its interest is as the first example of a nonlinear spin one field model in the plane that is integrable… …   Wikipedia 18+ © Academic, 2000-2024 Contact us: Technical Support, Advertising Dictionaries export, created on PHP, Joomla, Drupal, WordPress, MODx. Mark and share Search through all dictionaries Translate… Search Internet Share the article and excerpts Direct link … Do a right-click on the link above and select “Copy Link”