  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.
