A Unified Construction of Variational Methods for the Nonlinear Schroedinger Equation
Yeong E. Kim, Alexander L. Zubarev (Department of Ahysics, Purdue, University, West Lafayette)
TL;DR
This paper develops a systematic approach to construct variational principles for the nonlinear Schrödinger equation, including the Ginzburg-Pitaevskii-Gross equation, and proposes a variational iteration method for eigenvalue and wave function computation.
Contribution
It introduces a unified framework for variational methods applicable to nonlinear Schrödinger equations, including new principles for the GPG equation related to Bose-Einstein condensation.
Findings
New variational principles for GPG equation derived
Variational iteration method effectively computes eigenvalues and wave functions
Framework enhances accuracy and efficiency in solving nonlinear Schrödinger equations
Abstract
Based on an approach introduced byGerjuoy, Rau, and Spruch, we constract variational principles in a systematic way for the nonlinear Schroedinger equation and obtain new variational principles for the case of Ginzburg-Pitaevskii-Gross equation (PGP) which is belived to describe accurately the Bose-Einstein condensation at zero temperature. As an application of these variational methods, a variational iteration method is proposed for calculating eigenvalue (chemical potential) and wave function for the GPG equation
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Taxonomy
TopicsNumerical methods for differential equations