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Sine-Gordon equation
Nonlinear partial differential equation
Sine-Gordon equation
The sine-Gordon equation is a second-order nonlinear partial differential equation for a function φ {\displaystyle \varphi } dependent on two variables typically denoted x {\displaystyle x} and t {\displaystyle t} , involving the wave operator and the sine of φ {\displaystyle \varphi } . It was originally introduced by Edmond Bour (1862) in the course of study of surfaces of constant negative curvature as the Gauss–Codazzi equation for surfaces of constant Gaussian curvature −1 in 3-dimensional space. The equation was rediscovered by Yakov Frenkel and Tatyana Kontorova (1939) in their study of crystal dislocations known as the Frenkel–Kontorova model. This equation attracted a lot of attention in the 1970s due to the presence of soliton solutions, and is an example of an integrable PDE. Among well-known integrable PDEs...
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