HIERARCHIES AND HAMILTONIAN STRUCTURES OF THE NONLINEAR SCHRODINGER FAMILY USING GEOMETRIC AND SPECTRAL TECHNIQUES

Autor(es)

Guha, Partha ^{[1, 2]} ; Mukherjee, Indranil ^[3]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Inst Fis Sao Carlos, Caixa Postal 369, BR-13560970 Sao Carlos, SP - Brazil

^[2] SN Bose Natl Ctr Basic Sci, JD Block, Sect 3, Kolkata 700106 - India

^[3] Maulana Abul Kalam Azad Univ Technol, Sch Management & Sci, BF 142, Sect 1, Kolkata 700064 - India

• Tipo de documento: Artigo Científico
• Fonte: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B; v. 24, n. 4, p. 1677-1695, APR 2019.
• Citações Web of Science: 0

Resumo

This paper explores the class of equations of the Non-linear Schrodinger (NLS) type by employing both geometrical and spectral analysis methods. The work is developed in three stages. First, the geometrical method (AKS theorem) is used to derive different equations of the Non-linear Schrodinger (NLS) and Derivative Non-linear Schrodinger (DNLS) families. Second, the spectral technique (Tu method) is applied to obtain the hierarchies of equations belonging to these types. Third, the trace identity along with other techniques is used to obtain the corresponding Hamiltonian structures. It is found that the spectral method provides a simple algorithmic procedure to obtain the hierarchy as well as the Hamiltonian structure. Finally, the connection between the two formalisms is discussed and it is pointed out how application of these two techniques in unison can facilitate the understanding of integrable systems. In concurrence with Tu's method, Gesztesy and Holden also formulated a method of derivation of the trace formulas for integrable nonlinear evolution equations, this method is based on a contour-integration technique. (AU)

• Processo FAPESP: 16/06560-6 - Dinâmica não-linear e gravidade
• Beneficiário: Betti Hartmann
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Internacional