On the solutions of a general class of non-linear Schrödinger equations

Abstract

A successful strategy for the analytical study of the family of non-linear Schrödinger equations i ∂ψ/ ∂t+ ∂ su2ψ/∂x 2+g‖ ψ ψ‖ κψ=0 has been the linear delta expansion. Using this approach, the exact solution of the initial value problem ψ( x, t=0) = Cδ( x) is here obtained for the class of non-linear Schrödinger equations of the generalized form: i∂ψ/∂t + ∂ 2ψ/∂x 2 + (Σ j g j‖ ψψ‖ κj)ψ=0 .