The discrete nonlinear Schrödinger type hierarchy, its finite dimensional reduction analysis and numerical integrability scheme

• Дата: 2017
• Автори: Prykarpatsky, A.K., Cieśliński, J.
• Формат: Стаття
• Мова: English
• Опубліковано: Інститут математики НАН України 2017
• Назва видання: Нелінійні коливання
• Онлайн доступ: http://dspace.nbuv.gov.ua/handle/123456789/177304
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Цитувати: The discrete nonlinear Schrödinger type hierarchy, its finite dimensional reduction analysis and numerical integrability scheme / A.K. Prykarpatsky, J. Cieśliński // Нелінійні коливання. — 2017. — Т. 20, № 2. — С. 228-266 — Бібліогр.: 61 назв. — англ.

We investigate discretizations of the integrable nonlinear Schrodinger dynamical system, well known as the ¨ Ablowitz – Ladik equation, the related symplectic structures and its finite dimensional invariant reductions. An effective scheme of invariant reducing the corresponding infinite system of ordinary differential equations to an equivalent finite system of ordinary differential equations with respect to the evolution parameter is developed. A finite set of recurrent algebraic regular relations, allowing to generate solutions of the discrete nonlinear Schrodinger dynamical system, is constructed, the related functional spaces of ¨ solutions is discussed. Finally, the Fourier transform approach to studying the solution set of the discrete nonlinear Schrodinger dynamical system and its functional-analytical aspects is analyzed.