Related papers: Exact solutions to the focusing nonlinear Schrodin…
It is shown that using the similarity transformations, a set of three-dimensional p-q nonlinear Schrodinger (NLS) equations with inhomogeneous coefficients can be reduced to one-dimensional stationary NLS equation with constant or varying…
Recently developed simple approach for the exact/approximate solution of Schrodinger equations with constant/position-dependent mass, in which the potential is considered as in the perturbation theory, is shown to be equivalent to the one…
A nonlinear generalisation of Schrodinger's equation had previously been obtained using information-theoretic arguments. The nonlinearities in that equation were of a nonpolynomial form, equivalent to the occurence of higher-derivative…
We consider the cubic defocusing nonlinear Schr\"odinger equation in one dimension with the nonlinearity concentrated at a single point. We prove global well-posedness in the scaling-critical space $L^2(\mathbb{R})$ and scattering for all…
This paper is concerned with an alternative analytical solution of time-fractional nonlinear Schrodinger equation and nonlinear coupled Schrodinger equation obtained by employing fractional reduced differential transform method. The…
We prove the existence of global analytic solutions to the nonlinear Schr\"odinger equation in one dimension for a certain type of analytic initial data in $L^2$.
For the first time, a nonlinear Schr\"odinger equation of the general form is considered, depending on time and two spatial variables, the potential and dispersion of which are specified by two arbitrary functions. This equation naturally…
The aim of this work is to study the numerical solution of the nonlinear Schrodinger problem using a combination between Witt basis and finite difference approximations. We construct a discrete fundamental solution for the non-stationary…
Solutions of time-independent Schrodinger equation for potentials periodic in space satisfy Bloch theorem. The theorem has been used to obtain solutions of the Schrodinger equation for periodic systems by expanding them in terms of plane…
The time dependent complex Schr\"odinger equation with cubic nonlinearity is solved by constructing differential quadrature algorithm based on sinc functions. Reduction to a coupled system of real equations enables to approach the space…
The compact explicit expressions for formal exact operator solutions to Cauchy problem for sufficiently general systems of nonlinear differential equations (ODEs and PDEs) in the form of chronological operator exponents are given. The…
The outlook of a simple method to generate localized (soliton-like) potentials of time-dependent Schrodinger type equations is given. The conditions are discussed for the potentials to be real and nonsingular. For the derivative Schrodinger…
A certain symmetry is exploited in expressing exact solutions to the focusing nonlinear Schr\"odinger equation in terms of a triplet of constant matrices. Consequently, for any number of bound states with any number of multiplicities the…
Exact solutions of Schrodinger equation for PT-/non-PT-symmetric and non-Hermitian Morse and Poschl-Teller potentials are obtained with the position-dependent effective mass by applying a point canonical transformation method. Three kinds…
We here show how the methods recently applied by [DW16] to solve the stochastic nonlinear Schr\"odinger equation on $\mathbb{T}^2$ can be enhanced to yield solutions on $\mathbb{R}^2$ if the non-linearity is weak enough. We prove that the…
The asymptotic iteration method is used to find exact and approximate solutions of Schroedinger's equation for a number of one-dimensional trigonometric potentials (sine-squared, double-cosine, tangent-squared, and complex cotangent).…
We develop an approach to solving numerically the time-dependent Schrodinger equation when it includes source terms and time-dependent potentials. The approach is based on the generalized Crank-Nicolson method supplemented with an…
A method for the search of exact solutions for equation of a nonlocal scalar field in a non-flat metric is considered. In the Friedmann-Robertson-Walker metric the proposed method can be used in the case of an arbitrary potential, with the…
We present new approaches for solving constrained multicomponent nonlinear Schr\"odinger equations in arbitrary dimensions. The idea is to introduce an artificial time and solve an extended damped second order dynamic system whose…
Using canonical transformations we obtain localized (in space) exact solutions of the nonlinear Schr\"odinger equation (NLSE) with space and time modulated nonlinearity and in the presence of an external potential depending on space and…