Exact form of the Bogoliubov excitations in one-dimensional nonlinear Schrödinger equation

Exact Form of the Bogoliubov Excitations in One-dimensional Nonlinear Shrödinger Equation

In the paper we present the exact solutions of one-dimensional Non-linear Shrödinger Equation. The solutions correspond to the Bogoliubov excitations in Bose-gas with a local interaction. The obtained expression is used for evaluating the transmission coefficient of the excitations across a δ-functional potential barrier.

Numerical solution for one-dimensional independent of time Schrödinger Equation

In this paper, one of the numerical solution method of one- particle, one dimensional timeindependentSchrodinger equation are presented that allows one to obtain accurate bound state eigenvalues and functions for an arbitrary potential energy function V(x).For each case, we draw eigen functions versus the related reduced variable for the correspondingenergies. The paper ended with a comparison ...

numerical solution for one-dimensional independent of time schrödinger equation

in this paper, one of the numerical solution method of one- particle, one dimensional timeindependentschrodinger equation are presented that allows one to obtain accurate bound state eigenvalues and functions for an arbitrary potential energy function v(x).for each case, we draw eigen functions versus the related reduced variable for the correspondingenergies. the paper ended with a comparison ...

Direct search for exact solutions to the nonlinear Schrödinger equation

A five-dimensional symmetry algebra consisting of Lie point symmetries is firstly computed for the nonlinear Schrödinger equation, which, together with a reflection invariance, generates two five-parameter solution groups. Three ansätze of transformations are secondly analyzed and used to construct exact solutions to the nonlinear Schrödinger equation. Various examples of exact solutions with c...

Collapse of solitary excitations in the nonlinear Schrödinger equation with nonlinear damping and white noise.