The sine–Gordon equation is a nonlinear hyperbolic partial differential equation in 1 + 1 dimensions involving the d'Alembert operator and the sine of the unknown function. This equation attracted a lot of attention in the 1970s due to the presence of soliton solutions. It has importance in quantum field theory, topological aspects like soliton, instanton, in the integrable model, and in exact solutions like Beth ansatz.

The sine–Gordon equation is a nonlinear hyperbolic partial differential equation in 1 + 1 dimensions involving the d'Alembert operator and the sine of the unknown function.

This equation attracted a lot of attention in the 1970s due to the presence of soliton solutions. It has importance in quantum field theory, topological aspects like soliton, instanton, in the integrable model, and in exact solutions like Beth ansatz.

In quantum field theory the sine–Gordon model contains a parameter, it can be identified with Planck constant. The particle spectrum consists of a soliton, an anti-soliton and a finite (possibly zero) number of breathers. The number of the breathers depends on the value of the parameter. Multiparticle productions cancels on mass shell. Vanishing of two into four amplitude was explicitly checked in one-loop approximation. Semiclassical quantization of the sine–Gordon model was done by Ludwig Faddeev and Vladimir Korepin. The exact quantum scattering matrix was discovered by Alexander Zamolodchikov. This model is S-dual to the Thirring model. More on Wikipedia.

history | excerpt history