nLab
wave equation
Context
Differential geometry
Equality and Equivalence
equivalence

equality (definitional, propositional, computational, judgemental, extensional, intensional, decidable)

identity type, equivalence in homotopy type theory

isomorphism, weak equivalence, homotopy equivalence, weak homotopy equivalence, equivalence in an (∞,1)category

natural equivalence, natural isomorphism

gauge equivalence

Examples.
principle of equivalence
equation

fiber product, pullback

homotopy pullback

Examples.

linear equation, differential equation, ordinary differential equation, critical locus

EulerLagrange equation, Einstein equation, wave equation

Schrödinger equation, KnizhnikZamolodchikov equation, MaurerCartan equation, quantum master equation, EulerArnold equation, Fuchsian equation, FokkerPlanck equation, Lax equation
Contents
Idea
For $(X,g)$ a Riemannian manifold and $\Delta : C^\infty(X) \to C^\infty(X)$ its Laplace operator, the wave equation on $X$ is the differential equation
$\Delta f = 0
\,.$
where $\Delta$ is the wave operator /Laplace operator.
Revised on February 27, 2015 14:51:31
by
Urs Schreiber
(195.113.30.252)