Dispersive partial differential equation explained

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)
• Dispersionless equation

References

• Book: Erdoğan, M. Burak . Tzirakis . Nikolaos . Dispersive Partial Differential Equations . Cambridge University Press . Cambridge . 2016 . 978-1-107-14904-5.

External links

• The Dispersive PDE Wiki.