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After this manuscript was submitted, it came to my attention that equation (8) was recently derived by Staliunas following a different approach []. In his paper, equation (8) is derived directly from the model equations of reference [4] by adiabatic elimination of the pump field, and the presence of an imaginary part in the nonlinear term is due to a pump mistuning rather than a phase-mismatch as here
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Staliunas, K., 1995. J. Mod. Opt., 42:1261 After this manuscript was submitted, it came to my attention that equation (8) was recently derived by Staliunas following a different approach []. In his paper, equation (8) is derived directly from the model equations of reference [4] by adiabatic elimination of the pump field, and the presence of an imaginary part in the nonlinear term is due to a pump mistuning rather than a phase-mismatch as here.
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