Derivation of Nonlinear Schr\"{o}dinger Equation
Mathematical Physics
2011-04-04 v1 math.MP
Quantum Physics
Abstract
We propose some nonlinear Schr\"{o}dinger equations by adding some higher order terms to the Lagrangian density of Schr\"{o}dinger field, and obtain the Gross-Pitaevskii (GP) equation and the logarithmic form equation naturally. In addition, we prove the coefficient of nonlinear term is very small, i.e., the nonlinearity of Schr\"{o}dinger equation is weak.
Keywords
Cite
@article{arxiv.1104.0138,
title = {Derivation of Nonlinear Schr\"{o}dinger Equation},
author = {Xiang-Yao Wu and Bai-Jun Zhang and Xiao-Jing Liu and Li-Xiao and Yi-Heng Wu and Yan-Wang and Qing-Cai Wang and Shuang Cheng},
journal= {arXiv preprint arXiv:1104.0138},
year = {2011}
}