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Study boundary conditions and boundary effects for ATFT and their RHF

Investigate the types of boundary conditions and boundary effects for affine Toda field theories and for the corresponding real Hamiltonian forms derived via external automorphisms.

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Background

Boundary conditions play a crucial role in integrable field theories, influencing solution structures and scattering behavior. While integrable boundary conditions are known in some ATFT settings, their systematic treatment in the RHF context remains incomplete.

The authors explicitly flag the analysis of boundary conditions and boundary effects for ATFT and their RHF as an open problem, indicating a need for classification and detailed paper.

References

Another open problem is to study types of boundary conditions and boundary effects of ATFT’s and their RHF [10, 11].

— On affine Toda field theories related to ${\bf D}_r$ algebras and their real Hamiltonian forms (2401.18027 - Gerdjikov et al., 31 Jan 2024) in Section 5 (Conclusions)