In theoretical physics, the (one-dimensional) nonlinear Schrödinger equation (NLSE) is a nonlinear variation of the Schrödinger equation. Some simple recursive methods are described for constructing asymptotically exact solutions of the nonlinear Schrödinger equation (NLSE). In that case, you’d have the following equation: And you can […]

It is a classical field equation whose principal applications are to the propagation of light in nonlinear optical fibers and planar waveguides and to Bose–Einstein condensates confined to highly anisotropic cigar-shaped traps, in the mean-field regime. This work presents a novel numerical stability analysis of a collection of pseudo-spectral methods, also known as split-step methods, for solving pulse propagation modeled by the nonlinear Schrödinger equation in the nonlinear fiber optics formalism.

It is shown that the NLSE solution can be expressed analytically by two recurrence relations corresponding to two different perturbation methods.

In other words, this corresponds to a particle traveling freely through empty space. The discussion starts with the Schrödinger equation: Say you’re dealing with a free particle whose general potential, V(x) = 0. We study the inhomogeneous nonlinear time-fractional Schrödinger equation for linear potential, where the order of fractional time derivative parameter α varies between $0 < \alpha < 1$ .

All simulations are performed on a Windows 10 machine with Intel Core i5, 2.5 GHz, and 8 GB using MATLAB R2011b. The paper discusses approaches to the numerical integration of the second-kind Manakov equation system.

Emphasis is placed on the transition from writing equations in dimensional quantities to equations in dimensionless units.

Some simple recursive methods are described for constructing asymptotically exact solutions of the nonlinear Schrödinger equation (NLSE). In this section, we carry out several numerical examples to exhibit the performance of the proposed EFPS methods for solving the 2D NLS equation with a general nonlinear term. On the other hand, the pseudo-spectral methods, also known as split-step methods, are useful to solve the Schrödinger-type equation in a quantum formalism , as well as multiple nonlinear partial differential equations in different contexts such as the NLSE in nonlinear optics formalism , the complex cubic-quintic Ginzburg–Landau equation , the nonlinear Korteweg–de Vries equation [30, 31], … The most general form is the time-dependent Schrödinger equation (TDSE), which gives a description of a system evolving with time: A wave function that satisfies the nonrelativistic Schrödinger equation with V = 0.

Additionally, the equation appears in the studies of small-amplitude gravity waveson the surface of deep inviscid (zero-viscosity) … There are plenty of free particles — particles outside any square well —in the universe, and quantum physics has something to say about them. In order to guarantee the

First, we begin from the original Schrödinger equation, and then by the Caputo fractional derivative method in natural units, we introduce the fractional time-derivative Schrödinger equation.