wave equation

Any wave equation describes the propagation in space-time of a wave (or periodic motion, oscillation, `physical perturbation' or `signal') in terms of certain types of differential equations (such as partial differential ones); the solutions of such wave equations-usually with additonal boundary conditions- are either propagating or stationary waves; there are numerous types of waves, and thus, there are many different types of wave equations. The following is a short list of such wave equations, that is however not intended to be comprehensive.

Types of Wave Equations:

  1. Elastic wave equation and Hook's Law

  2. Equation for sound wave propagation

  3. Wave equation for heat transfer;

  4. Laplace wave equation;

  5. Maxwell's equations for electromagnetic wave propagation;

  6. Schrödinger 'wave' equation for electrons (see also Hamiltonian operator);

  7. Heisenberg's quantum dynamic equations (see also Hamiltonian operator and quantum harmonic oscillator and Lie algebra);

  8. Dirac relativistic wave equation;

  9. soliton wave equations;

  10. spin wave equations;

  11. Einstein's gravitational wave equations;

Examples:

In its simplest form, the wave equation refers to a scalar function $ w$ that satisfies:

$ \partial^2 (w) \over {\partial t^2}$ = $ c^2 \nabla^2 u,$

where $ \nabla^2$ is the Laplace operator, and where $ c$ is a fixed constant equal to the propagation speed of the wave.



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As of this snapshot date, this entry was owned by bloftin.