Classical Darboux transform

Function to generate multi-soliton solutions of NLSE using CDT

The nonlinear Schrodinger equation (NLSE) models the propagation of light in nonlinear optical fibers and planar waveguides. NLSE has so called multi-soliton solutions which do not have any continuous spectrum and can be defined using only the discrete spectrum which consists of the eigenvalues and norming constants. The classical Darboux transform is the standard method for generating multi-solitons [1]. The Algorithm 2 given in [2] is implemented with some modifications to improve numerical conditioning. The order in which the eigenvalues are added is based on the observations in [3]. Such an ordering greatly reduces round-off errors.
References:
1. J. Lin, “Evolution of the scattering data under the classical Darboux transform for su(2)
soliton systems,” Acta Mathematicae Applicatae Sinica, vol. 6, no. 4, pp. 308–316, 1990.
2. V. Aref, “Control and detection of discrete spectral amplitudes in nonlinear fourier spectrum.”
https://arxiv.org/abs/1605.06328v1, 2017. Accessed: 18-04-2017.
3. V. Vaibhav and S. Wahls, “Multipoint newton-type nonlinear fourier transform for detecting
multi-solitons,” in 2016 Optical Fiber Communications Conference and Exhibition
(OFC), pp. 1–3, March 2016.