# Systems, Environments, and Soliton Rate Equations: Toward Realistic Modeling

@article{Kuna2018SystemsEA,
title={Systems, Environments, and Soliton Rate Equations: Toward Realistic Modeling},
author={Maciej Kuna},
journal={Foundations of Science},
year={2018},
volume={24},
pages={95-132}
}
• M. Kuna
• Published 12 March 2018
• Physics, Biology
• Foundations of Science
In order to solve a system of nonlinear rate equations one can try to use some soliton methods. The procedure involves three steps: (1) find a ‘Lax representation’ where all the kinetic variables are combined into a single matrix $$\rho$$ρ, all the kinetic constants are encoded in a matrix H; (2) find a Darboux–Bäcklund dressing transformation for the Lax representation $$i{{\dot{\rho }}}=[H,f(\rho )]$$iρ˙=[H,f(ρ)], where f models a time-dependent environment; (3) find a class of seed solutions…

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