Abstract: In this paper, a perturbing nonlinear homogeneous Schrodinger equation is studied under limited time interval, complex initial conditions and zero Neumann conditions. The perturbation and Picard approximation methods together with the eigenfunction expansion and variational parameters methods are used to introduce an approximate solution for the perturbative nonlinear case for which a...

In this paper we consider solutions of a nonlinear Schrodinger equation with a parabolic and a periodic potential motivated from the dynamics of Bose-Einstein condensates. Our starting point is the corresponding linear problem which we analyze through regular perturbation and homogenization techniques. We then use Lyapunov-Schmidt theory to establish the persistence and bifurcation of the linea...

We study the conditions for soliton-like wave propagation in the Photorefractive (PR) and electro-optic (i.e., Pockels) material, by using Nonlinear Schrodinger (NLS) equation. The complete NLS equation is solved analytically and numerically by transforming it into the phase space. Our results clearly show the existence of both the dark and bright solitary solutions for the PR medium. Interesti...

The standard quantum discrete nonlinear Schrodinger equation with periodic boundary conditions and an arbitrary number of freedoms (f) is solved exactly at the second and third quantum levels. I f f -+ x at a sufficiently small level of anharmonicity c j ) , the value for soliton binding energy from quantum field‘theory (QFT) in the continuum limit is recovered. For fixed however, the QFT resul...

We show the global well-posedness of nonlinear Schrodinger equation with periodically varying coefficients and a small parameter ɛ > 0, which is used in optical-fiber communications. also prove that solutions converge to solution for Gabitov–Turitsyn or averaged as tends zero.

It is unnecessary, nowadays, to point out the importance of the Schrodinger equation to disciplines of science and technology. In principle, one can understand any natural phenomenon if one can solve the corresponding Schrodinger equations. Unfortunately, the Schrodinger equation can only be analytically solved in a few special cases. Therefore, it is very important to know the properties of th...