2005/10/20 by Victor M. Perez-Garcia, Víctor M. Pérez‐García, Pedro J. Torres +5 · 1 citation
Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Pattern Formation and Solitons (nlin.PS) #Quantum chaos and dynamical systems #math-ph #math.MP #nlin.PS #nlin.SI
paper · pdf · doi:10.48550/arxiv.nlin/0510044
arxiv created 2005/10/20 · openalex publication_date 2005/10/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The method of moments in the context of Nonlinear Schrodinger Equations relies on defining a set of integral quantities, which characterize the solution of this partial differential equation and whose evolution can be obtained from a set of ordinary differential equations. In this paper we find all cases in which the method of moments leads to closed evolution equations, thus extending and unifying previous works in the field of applications. For some cases in which the method fails to provide rigorous information we also develop approximate methods based on it, which allow to get some approximate information on the dynamics of the solutions of the Nonlinear Schrodinger equation.