Self-trapping on a dimer: Time-dependent solutions of a discrete nonlinear Schrödinger equation.

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Analytical Soliton Solutions Modeling of Nonlinear Schrödinger Equation with the Dual Power Law Nonlinearity  

Introduction In this study, we use a newly proposed method based on the software structure of the maple, called the Khaters method, and will be introducing exponential, hyperbolic, and trigonometric solutions for one of the Schrödinger equations, called the nonlinear Schrödinger equation with the dual power law nonlinearity. Given the widespread use of the Schrödinger equation in physics and e...

A Local Strong form Meshless Method for Solving 2D time-Dependent Schrödinger Equations

This paper deals with the numerical solutions of the 2D time dependent Schr¨odinger equations by using a local strong form meshless method. The time variable is discretized by a finite difference scheme. Then, in the resultant elliptic type PDEs, special variable is discretized with a local radial basis function (RBF) methods for which the PDE operator is also imposed in the local matrices. Des...

Time evolution of models described by a one-dimensional discrete nonlinear Schrödinger equation.

The dynamics of models described by a one-dimensional discrete nonlinear Schrödinger equation is studied. The nonlinearity in these models appears due to the coupling of the electronic motion to optical oscillators which are treated in adiabatic approximation. First, various sizes of nonlinear cluster embedded in an infinite linear chain are considered. The initial excitation is applied either ...

Wave energy self-trapping by self-focusing in large molecular structures: A damped stochastic discrete nonlinear Schrödinger equation model

Wave self-focusing in molecular systems subject to thermal effects, such as thin molecular films and long biomolecules, can be modeled by stochastic versions of the discrete self-trapping equation of Eilbeck et al. [J.C. Eilbeck, P.S. Lomdahl, A.C. Scott, The discrete self-trapping equation, Physica D 16 (1985) 318–338], which gives as a continuum limit approximation the stochastic nonlinear Sc...