Coupling the Sine-Gordon Field Theory to a Mechanical System at the Boundary

Details Coupling the Sine-Gordon Field Theory to a Mechanical System at the Boundary Coupling the Sine-Gordon Field Theory to a Mechanical System at the Boundary

2002-01-07

arxiv.org/abs/nlin/0201007v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

9 pages, Contribution to the proceedings of the NATO Advanced Research Workshop on Statistical Field Theories 2001

Scientific paper

We describe an integrable system consisting of the sine-Gordon field, restricted to the half line, and coupled to a non-linear oscillator at the boundary. By extension of the coupling constant to imaginary values we also outline the equivalent system for the sinh-Gordon field. We show how Sklyanin's formalism can be applied to situations with dynamic boundary conditions, and illustrate the method with the derivation of our example system.

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