# Helmholtz equation

From AMS Glossary

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## Helmholtz equation

A linear second-order partial differential equation of the form where ∇

^{2}is the Laplacian operator and*k*is a constant.This equation occurs frequently in dynamic meteorology, for example, in numerical forecasting or in the study of lee waves. In classical physics it is the equation of the vibrating membrane. The case

*k*= 0 reduces to a Laplace equation.