Elliptic solutions, gauge normal forms and a degenerate four-wave-mixing projection for coherent couplers
Year: 2026
Type: preprint
Abstract: We relate a complex Hamiltonian extension of the asymmetric conservative coherent coupler to three-mode degenerate four-wave mixing. A trajectory-dependent reciprocal gauge preserves the modal products and gives an autonomous normal form with meromorphic envelopes; we construct a projection from degenerate four-wave mixing onto this normal form. Building on established elliptic power-transfer and phase descriptions, we reconstruct the complex envelopes explicitly in Weierstrass $σ$ and $ζ$ functions for unequal propagation constants and self-phase coefficients with symmetric cross-phase coupling. This representation exposes the noninteger powers of sigma ratios introduced generically by unequal self-phase coefficients, and their removal by the gauge. The lifted modes are exponentially gauged Kronecker kernels, equivalently genus-one Baker-Akhiezer functions, and the conserved Hamiltonian product relation is represented by a four-point Frobenius-Stickelberger determinant identity. These mode-level relationships place the coupler within a wider family of integrable continuous-wave systems; numerical comparisons verify the formulae and their evaluation.
Source: arXiv (Cornell University)
Author: Hesketh, Graham
Language: English
Topic: Nonlinear Waves and Solitons
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7161774521