Differential-algebraic approach to constructing representations of commuting differentiations in functional spaces and its application to nonlinear integrable dynamical systems

Prykarpatski, Anatolij; Soltanov, Kamal; ÖZÇAĞ, EMİN

doi:10.1016/j.cnsns.2013.09.029

Differential-algebraic approach to constructing representations of commuting differentiations in functional spaces and its application to nonlinear integrable dynamical systems

Prykarpatski A. K., Soltanov K. N., ÖZÇAĞ E.

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, cilt.19, sa.5, ss.1644-1649, 2014 (SCI-Expanded, Scopus)

Yayın Türü: Makale / Tam Makale
Cilt numarası: 19 Sayı: 5
Basım Tarihi: 2014
Doi Numarası: 10.1016/j.cnsns.2013.09.029
Dergi Adı: COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
Sayfa Sayıları: ss.1644-1649
Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
Hacettepe Üniversitesi Adresli: Evet

Özet

There is developed a differential-algebraic approach to studying the representations of commuting differentiations in functional differential rings under nonlinear differential constraints. An example of the differential ideal with the only one conserved quantity is analyzed in detail, the corresponding Lax type representations of differentiations are constructed for an infinite hierarchy of nonlinear dynamical systems of the Burgers and Korteweg-de Vries type. A related infinite bi-Hamiltonian hierarchy of Lax type dynamical systems is constructed. (C) 2013 Elsevier B.V. All rights reserved.