Integrable boundary conditions for classical sine-Gordon theory

Abstract

The possible boundary conditions consistent with the integrability of the classical sine-Gordon equation are studied. A boundary value problem on the half-line $x\le 0$ with local boundary condition at the origin is considered. The most general form of this boundary condition is found such that the problem be integrable. For the resulting system an infinite number of involutive integrals of motion exist. These integrals are calculated and one is identified as the Hamiltonian. The results found agree with some recent work of Ghoshal and Zamolodchikov.

10 pages, DTP/94-39

References in corpus (4)

• Boundary S-Matrix and Boundary State in Two-Dimensional Integrable Quantum Field Theory
• Affine Toda field theory on a half line
• Factorized Scattering in the Presence of Reflecting Boundaries
• Boundary S-matrix of the $O(N)$-symmetric Non-linear Sigma Model

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