Related papers: Exact solutions to the focusing nonlinear Schrodin…
A review of a recent method is presented to construct certain exact solutions to the focusing nonlinear Schr\"odinger equation on the line with a cubic nonlinearity. With motivation by the inverse scattering transform and help from the…
A procedure of solving nonstationary Schredinger equations in the exact analytic form is elaborated on the basis of exactly solvable stationary models. The exact solutions are employed to study the nonadiabatic geometric phase.
We outline a general method of obtaining exact solutions of Schroedinger equations with a position dependent effective mass. Exact solutions of several potentials including shape invariant potentials have also been obtained.
A method is presented to construct exactly solvable nonlinear extensions of the Schr\"odinger equation. The method explores a correspondence which can be established under certain conditions between exactly solvable ordinary Schr\"odinger…
A method to find exact solutions to nonlinear Schr\"odinger equation, defined on a line and on a plane, is found by connecting it with second order linear ordinary differential equation. The connection is essentially made using Riccati…
The aim of this paper is to find the exact solutions of the Schrodinger equation. As is known, the Schrodinger equation can be reduced to the continuum equation. In this paper, using the non-linear Legendre transform the equation of…
In this paper, we investigate the numerical solutions of the cubic nonlinear Schrodinger equation via the exponential B-spline collocation method. Crank-Nicolson formulas are used for time discretization of the target equation. A…
We show that the thermodynamics of the focusing cubic discrete nonlinear Schrodinger equation are exactly solvable in dimensions three and higher. A number of explicit formulas are derived.
We obtain exact solutions to the class of parabolic partial differential equations of arbitrary dimensionality and with arbitrary potentials. The solutions are presented in a compact-form: as explicit mathematical expressions consisting of…
Explicit solutions are obtained for a class of semilinear radial Schrodinger equations with power nonlinearities in multi-dimensions. These solutions include new similarity solutions and other new group-invariant solutions, as well as new…
A five-dimensional symmetry algebra consisting of Lie point symmetries is firstly computed for the nonlinear Schroedinger equation, which, together with a reflection invariance, generates two five-parameter solution groups. Three ansaetze…
In this paper, we acquire the soliton solutions of the nonlinear Schrodinger's equation with dual power-law nonlinearity. Primiraly, we use the extended trial equation method to find exact solutions of this equation. Then, we attain some…
We consider construction of ansatzes for nonlinear Schrodinger equations in three space dimensions and arbitrary nonlinearity, and conditions of their reduction to ordinary differential equations. Complete description of ansatzes of certain…
We review an explicit approach to obtaining numerical solutions of the Schr\"odinger equation that is conceptionally straightforward and capable of significant accuracy and efficiency. The method and its efficacy are illustrated with…
For the first time, Schr\"odinger equations with cubic and more complex nonlinearities containing the unknown function with constant delay are analyzed. The physical considerations that can lead to the appearance of a delay in such…
Using similarity transformations we construct explicit solutions of the nonlinear Schrodinger equation with linear and nonlinear periodic potentials. We present explicit forms of spatially localized and periodic solutions, and study their…
The method of solving of nonlinear Schr\"odinger equation is considered. Some examples of its applications are demonstrated.
In [8], some exact splittings are proposed for inhomogeneous quadratic differential equations including, for example, transport equations, kinetic equations, and Schr{\"o}dinger type equations with a rotation term. In this work, these exact…
For the first time, the general nonlinear Schr\"odinger equation is investigated, in which the chromatic dispersion and potential are specified by two arbitrary functions. The equation in question is a natural generalization of a wide class…
We study the presence of exact localized solutions in a quadratic-cubic nonlinear Schr\"odinger equation with inhomogeneous nonlinearities. Using a specific ansatz, we transform the nonautonomous nonlinear equation into an autonomous one,…