STANDING WAVE SOLUTIONS IN TWISTED MULTICORE FIBERS

Both the paper and the candidate solution derive the standing-wave amplitude–phase system, impose parity-dependent phase conditions at φ = π/N so that the sine constraints vanish and all surviving coupling phases equal +1 (except where the neighboring amplitude is identically zero at the prescribed dark site), reduce to a real, finite-dimensional system, and then apply the finite-dimensional Implicit Function Theorem near the AC limit k = 0 to obtain a smooth solution branch for small |k|. This is exactly what the paper does in Sec. 3.1–3.2 after writing the stationary equations (5)–(6) and reducing to (11) for even N and (15) for odd N; it then checks invertibility of the diagonal Jacobians and invokes IFT (after (11) and (15)) to conclude existence for sufficiently small k . The candidate solution mirrors this argument. Minor issues: the candidate’s displayed complex stationary equation once has a sign typo on the ω-term, while the paper has a small misprint in the odd-N AC seed; neither affects the existence argument or conclusion.