schrödinger's equation
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Author(s):  
Nauman Raza ◽  
Ahmad Javid ◽  
Asma Rashid Butt ◽  
Haci Mehmet Baskonus

Abstract This paper concerns with the integrability of variable coefficient fifth order nonlinear Schrödinger’s equation describing the dynamics of attosecond pulses in inhomogeneous fibers. Variable coefficients incorporate varying dispersion and nonlinearity which are of physical significance in considering the nonuniform boundaries of fibers as well as the inhomogeneities of the media. The well-known exp(−φ(s))-expansion method is used to retrieve singular and periodic solitons with the aid of symbolic computation. The structures of the obtained solutions are discussed along with their existence criteria. Moreover, the modulation instability analysis is carried out to identify the instability regions. A dispersion relation is extracted between wave number and frequency. The optimal value of the frequency is found for the occurrence of the instability. A detailed discussion of the results is also given along with graphics.


Author(s):  
M. Eslami ◽  
A. Neirameh

The generalized exponential rational function method, which is one of the strong methods for solving nonlinear evolution equations, is applied to the conformable resonant nonlinear Schrödinger’s equation in this study. This equation plays a significant role in nonlinear fiber optics. It also has many important applications in photonic crystal fibers. The procedure implemented in this paper can be recommended in solving other equations in the field. All calculations and graphing are performed using powerful symbolic computational packages in Mathematica software. All calculations and graphing are performed using powerful symbolic computational packages in Mathematica software.


2021 ◽  
Vol 81 (10) ◽  
Author(s):  
Abrar Ahmed Naqash ◽  
Barun Majumder ◽  
Soumodeep Mitra ◽  
Moomin Mushtaq Bangle ◽  
Mir Faizal

AbstractIn this paper, we analyze the correction to the mean field theory potential for a system of nucleons. It will be argued that these corrections can be obtained by deforming the Schrödinger’s equation describing a system of nucleons by a minimal length in the background geometry of space-time. This is because such a minimal length occurs due to quantum gravitational effects, and modifies the low energy quantum mechanical systems. In fact, as the mean field potential for the nucleons is represented by the Woods–Saxon potential, we will explicitly analyze such corrections to this potential. We will obtain the corrections to the energy eigenvalues of the deformed Schrödinger’s equation for the Woods–Saxon potential. We will also construct the wave function for the deformed Schrödinger’s equation.


2021 ◽  
Author(s):  
Gérard Gouesbet

It is well known that, by taking a limit of Schrödinger’s equation, we may recover Hamilton-Jacobi’s equation which governs one of the possible formulations of classical mechanics. Conversely, we may start from the Hamilton-Jacobi’s equation and, by using a lifting principle, we may reach a set of nonlinear generalized Schrödinger’s equations. The classical Schrödinger’s equation then occurs as the simplest equation among the set.


2021 ◽  
Author(s):  
Aman Yadav

The relationship between Einstein's Field Equation and Schrodinger's Equation is examined in thiswork. I adjusted Schrodinger's Equation to offer the solution, and utilizing the wave equation, Icame up with two cases: In case 1, I discovered the structure and dimension of the equations in amanner similar to Einstein's Field Equation, and in case 2, the Helmholtz equation replaces themodified Schrodinger's equation. Finally, the findings suggested that wave functions may haverelevance beyond determining the position of a particle, and that they may be used to determinethe structure of space-time at the quantum level.


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