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
In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats.
It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, t ...
propagate at different
phase velocities.
Examples
Linear equations
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Euler–Bernoulli beam equation with time-dependent loading
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Airy equation
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Schrödinger equation
The Schrödinger equation is a linear partial differential equation that governs the wave function of a quantum-mechanical system. It is a key result in quantum mechanics, and its discovery was a significant landmark in the development of th ...
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Klein–Gordon equation
The Klein–Gordon equation (Klein–Fock–Gordon equation or sometimes Klein–Gordon–Fock equation) is a relativistic wave equation, related to the Schrödinger equation. It is second-order in space and time and manifestly Lorentz-covariant ...
Nonlinear equations
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nonlinear Schrödinger equation
In theoretical physics, the (one-dimensional) nonlinear Schrödinger equation (NLSE) is a nonlinear variation of the Schrödinger equation. It is a classical field equation whose principal applications are to the propagation of light in nonlin ...
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Korteweg–de Vries equation (or KdV equation)
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Boussinesq equation (water waves)
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sine–Gordon equation
See also
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Dispersion (optics)
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Dispersion (water waves)
In fluid dynamics, dispersion of water waves generally refers to frequency dispersion, which means that waves of different wavelengths travel at different phase speeds. Water waves, in this context, are waves propagating on the water surface, ...
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Dispersionless equation
External links
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Dispersive PDE Wiki
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Partial differential equations
Nonlinear systems