Derivation of Nonlinear Schr\"odinger Equation
Abstract
We propose some nonlinear Schr\"odinger equations by adding some higher order terms to the Lagrangian density of Schr\"odinger 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\"odinger equation is weak.
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