In light-cone coordinates, the sine-Gordon equation can be written . Its inverse scattering transform, solitons, breathers, and scaling symmetries make it an integrable system.
The transformations
(1)
form a one-parameter Lie point symmetry of . The product is a similarity variable, and a group-invariant solution satisfies
(2)
For every ,
(1)
solves . The scaling transforms by multiplication with .
A sine-Gordon breather is a spatially localized solution that is periodic in time and can be interpreted through a complex-conjugate pair of discrete scattering eigenvalues.

Ancestors (4)

  1. Integrable systems
  2. Branch of physics
  3. Physics
  4. Home

Incoming links (9)

View article source

Discussion (0)

New discussion

There are no discussions about this article yet.

Articles by others on the same topic (1)

Sine-Gordon equation by Wikipedia Bot 1
View more
The sine-Gordon equation is a nonlinear partial differential equation of the form: \[ \frac{\partial^2 \phi}{\partial t^2} - \frac{\partial^2 \phi}{\partial x^2} + \sin(\phi) = 0 \] where \(\phi\) is a function of two variables, time \(t\) and spatial coordinate \(x\).
Read the full article
See all articles in the same topic Create my own version