Algorithm for finding soliton solutions of the equations like nonlinear Shroedinger equation
"Математика. Компьютер. Образование". Cб. трудов XII международной конференции. Под общей редакцией Г.Ю. Ризниченко Ижевск: Научно-издательский центр "Регулярная и хаотическая динамика", 2005. Vol. 2, 466pp. Pp. 640-647.
There can be various modifications of nonlinear Shroedinger equation corresponding to different physical systems. Besides the ordinary Shroedinger equation there can equations on a discrete lattice or nonlocal equations. The latter appears, for example, in the problem of proton tunneling in the hydrogen bonds if the DNA molecule. The resulting discrete nonlocal equation is obtained with the help of Davydov theory. The usual methods for finding soliton solutions can be used in the case of long waves only, and therefore cannot be utilized for the scale of the distance between the base pairs.
In this paper the following idea is used: the solution close enough to soliton consists of the central peak and the additional radiation of low amplitude. For the exact soliton solution this radiation is absent, thus giving us the measure of the solution purity. The exact solution can be obtained if the radiation is damped with the special filter. This method for finding soliton solutions appears to have wide applications.