Of Nonlinear Schrödinger Equations

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...

Quasilinear Schrödinger equations involving critical exponents in $mathbb{textbf{R}}^2$

‎We study the existence of soliton solutions for a class of‎ ‎quasilinear elliptic equation in $mathbb{textbf{R}}^2$ with critical exponential growth‎. ‎This model has been proposed in the self-channeling of a‎ ‎high-power ultra short laser in matter‎.

Existence of infinitely many solutions for coupled system of Schrödinger-Maxwell's equations

On a class of nonlinear fractional Schrödinger-Poisson systems

In this paper, we are concerned with the following fractional Schrödinger-Poisson system:    (−∆s)u + V (x)u + φu = m(x)|u|q−2|u|+ f(x,u), x ∈ Ω, (−∆t)φ = u2, x ∈ Ω, u = φ = 0, x ∈ ∂Ω, where s,t ∈ (0,1], 2t + 4s > 3, 1 < q < 2 and Ω is a bounded smooth domain of R3, and f(x,u) is linearly bounded in u at infinity. Under some assumptions on m, V and f we obtain the existence of non-trivial so...

Similarity transformations for Nonlinear Schrödinger Equations with time varying coefficients : Exact results

In this paper we use a similarity transformation connecting some families of Nonlinear Schrödinger equations with time-varying coefficients with the autonomous cubic nonlinear Schrödinger equation. This transformation allows one to apply all known results for that equation to the original non-autonomous case with the additional dynamics introduced by the transformation itself. In particular, us...