4 papers
Hyperelliptic sigma solutions of polynomial Hamiltonian systems
Graham Hesketh
We study polynomial Hamiltonian systems whose Hamiltonians consist of two weighted products of canonical modes minus a polynomial in their powers. This class extends the structure…
Elliptic solutions, gauge normal forms and a degenerate four-wave-mixing projection for coherent couplers
Graham Hesketh
We relate a complex Hamiltonian extension of the asymmetric conservative coherent coupler to three-mode degenerate four-wave mixing. A trajectory-dependent reciprocal gauge preserv…
Elliptic normal forms and Frobenius-Stickelberger identities for continuous-wave four-wave mixing
Graham Hesketh
We study the Hamiltonian and elliptic-function structure of continuous-wave four-wave mixing in nonlinear optical fibres. For the generic quartic reduction, we express the full com…
General complex envelope solutions of coupled-mode optics with quadratic or cubic nonlinearity
Graham D Hesketh
The analytic general solutions for the complex field envelopes are derived using Weierstrass elliptic functions for two and three mode systems of differential equations coupled via…