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The boundary conditions with diagonal boundary $S$ matrix and the boundaryform factors for the Smirnov--Fateev model on a half line has been consideredin the framework of the free field representation. In contrast to the case ofthe sine-Gordon model, in this case the free field representation is shown toimpose severe restrictions on the boundary $S$ matrix, so that a finite numberof solutions is only consistent with the free field realization.

Boundary form factors in the Smirnov--Fateev model with a diagonal boundary $S$ matrix