**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**1495

# Search results for: Coupled Schrödinger equation

##### 1495 Numerical Study of Some Coupled PDEs by using Differential Transformation Method

**Authors:**
Reza Abazari,
Rasool Abazari

**Abstract:**

In this paper, the two-dimension differential transformation method (DTM) is employed to obtain the closed form solutions of the three famous coupled partial differential equation with physical interest namely, the coupled Korteweg-de Vries(KdV) equations, the coupled Burgers equations and coupled nonlinear Schrödinger equation. We begin by showing that how the differential transformation method applies to a linear and non-linear part of any PDEs and apply on these coupled PDEs to illustrate the sufficiency of the method for this kind of nonlinear differential equations. The results obtained are in good agreement with the exact solution. These results show that the technique introduced here is accurate and easy to apply.

**Keywords:**
Coupled Korteweg-de Vries(KdV) equation,
Coupled Burgers equation,
Coupled Schrödinger equation,
differential transformation method.

##### 1494 Approximate Solution to Non-Linear Schrödinger Equation with Harmonic Oscillator by Elzaki Decomposition Method

**Authors:**
Emad K. Jaradat,
Ala’a Al-Faqih

**Abstract:**

Nonlinear Schrödinger equations are regularly experienced in numerous parts of science and designing. Varieties of analytical methods have been proposed for solving these equations. In this work, we construct an approximate solution for the nonlinear Schrodinger equations, with harmonic oscillator potential, by Elzaki Decomposition Method (EDM). To illustrate the effects of harmonic oscillator on the behavior wave function, nonlinear Schrodinger equation in one and two dimensions is provided. The results show that, it is more perfectly convenient and easy to apply the EDM in one- and two-dimensional Schrodinger equation.

**Keywords:**
Non-linear Schrodinger equation,
Elzaki decomposition method,
harmonic oscillator,
one and two- dimensional Schrodinger equation.

##### 1493 An Expansion Method for Schrödinger Equation of Quantum Billiards with Arbitrary Shapes

**Authors:**
İnci M. Erhan

**Abstract:**

**Keywords:**
Bessel functions,
Eigenfunction expansion,
Quantum billiard,
Schrödinger equation,
Spherical harmonics

##### 1492 Constructing Distinct Kinds of Solutions for the Time-Dependent Coefficients Coupled Klein-Gordon-Schrödinger Equation

**Authors:**
Anupma Bansal

**Abstract:**

We seek exact solutions of the coupled Klein-Gordon-Schrödinger equation with variable coefficients with the aid of Lie classical approach. By using the Lie classical method, we are able to derive symmetries that are used for reducing the coupled system of partial differential equations into ordinary differential equations. From reduced differential equations we have derived some new exact solutions of coupled Klein-Gordon-Schrödinger equations involving some special functions such as Airy wave functions, Bessel functions, Mathieu functions etc.

**Keywords:**
Klein-Gordon-Schödinger Equation,
Lie Classical Method,
Exact Solutions

##### 1491 Bound State Solutions of the Schrödinger Equation for Hulthen-Yukawa Potential in D-Dimensions

**Authors:**
I. Otete,
A. I. Ejere,
I. S. Okunzuwa

**Abstract:**

In this work, we used the Hulthen-Yukawa potential to obtain the bound state energy eigenvalues of the Schrödinger equation in D-dimensions within the frame work of the Nikiforov-Uvarov (NU) method. We demonstrated the graphical behaviour of the Hulthen and the Yukawa potential and investigated how the screening parameter and the potential depth affected the structure and the nature of the bound state eigenvalues. The results we obtained showed that increasing the screening parameter lowers the energy eigenvalues. Also, the eigenvalues acted as an inverse function of the potential depth. That is, increasing the potential depth reduces the energy eigenvalues.

**Keywords:**
Schrödinger's equation,
bound state,
Hulthen-Yukawa potential,
Nikiforov-Uvarov,
D-dimensions

##### 1490 An H1-Galerkin Mixed Method for the Coupled Burgers Equation

**Authors:**
Xianbiao Jia,
Hong Li,
Yang Liu,
Zhichao Fang

**Abstract:**

In this paper, an H1-Galerkin mixed finite element method is discussed for the coupled Burgers equations. The optimal error estimates of the semi-discrete and fully discrete schemes of the coupled Burgers equation are derived.

**Keywords:**
The coupled Burgers equation,
H1-Galerkin mixed
finite element method,
Backward Euler's method,
Optimal error
estimates.

##### 1489 Photon Localization inside a Waveguide Modeled by Uncertainty Principle

**Authors:**
Shilpa N. Kulkarni,
Sujata R. Patrikar

**Abstract:**

**Keywords:**
photon localization in waveguide,
photon tunneling,
quantum confinement of light,
Schrödinger wave equation,
uncertainty principle.

##### 1488 Calculation of Wave Function at the Origin (WFO) for Heavy Mesons by Numerical Solving of the Schrodinger Equation

**Authors:**
M. Momeni Feyli

**Abstract:**

**Keywords:**
Mesons,
Bound states,
Schrodinger equation,
Nonrelativistic
quark model.

##### 1487 FWM Wavelength Conversion Analysis in a 3-Integrated Portion SOA and DFB Laser using Coupled Wave Approach and FD-BPM Method

**Authors:**
M. K. Moazzam,
A. Salmanpour,
M. Nirouei

**Abstract:**

**Keywords:**
distributed feedback laser,
nondegenerate fourwave mixing,
semiconductor optical amplifier,
wavelengthconversion

##### 1486 Mathematical Approach for Large Deformation Analysis of the Stiffened Coupled Shear Walls

**Authors:**
M. J. Fadaee,
H. Saffari,
H. Khosravi

**Abstract:**

**Keywords:**
Buckling load,
differential equation,
energy method,
geometrically nonlinear analysis,
mathematical method,
Stiffened
coupled shear walls.

##### 1485 CO-OFDM DSP Channel Estimation

**Authors:**
Pranav Ravikumar,
Arunabha Bera,
Vijay K. Mehra,
Anand Kumar

**Abstract:**

**Keywords:**
Modulation,
Non Linear Schrodinger Equation,
Optical fiber,
Split Step Fourier Method.

##### 1484 Instability of Soliton Solutions to the Schamel-nonlinear Schrödinger Equation

**Authors:**
Sarun Phibanchon,
Michael A. Allen

**Abstract:**

A variational method is used to obtain the growth rate of a transverse long-wavelength perturbation applied to the soliton solution of a nonlinear Schr┬¿odinger equation with a three-half order potential. We demonstrate numerically that this unstable perturbed soliton will eventually transform into a cylindrical soliton.

**Keywords:**
Soliton,
instability,
variational method,
spectral method.

##### 1483 Impact of the Existence of One-Way Functionson the Conceptual Difficulties of Quantum Measurements

**Authors:**
Arkady Bolotin

**Abstract:**

**Keywords:**
One-way functions,
P versus NP problem,
quantummeasurements.

##### 1482 Stability of Stochastic Model Predictive Control for Schrödinger Equation with Finite Approximation

**Authors:**
Tomoaki Hashimoto

**Abstract:**

**Keywords:**
Optimal control,
stochastic systems,
quantum systems,
stabilization.

##### 1481 Schrödinger Equation with Position-Dependent Mass: Staggered Mass Distributions

**Authors:**
J. J. Peña,
J. Morales,
J. García-Ravelo,
L. Arcos-Díaz

**Abstract:**

The Point canonical transformation method is applied for solving the Schrödinger equation with position-dependent mass. This class of problem has been solved for continuous mass distributions. In this work, a staggered mass distribution for the case of a free particle in an infinite square well potential has been proposed. The continuity conditions as well as normalization for the wave function are also considered. The proposal can be used for dealing with other kind of staggered mass distributions in the Schrödinger equation with different quantum potentials.

**Keywords:**
Free particle,
point canonical transformation method,
position-dependent mass,
staggered mass distribution.

##### 1480 A Novel System of Two Coupled Equations for the Longitudinal Components of the Electromagnetic Field in a Waveguide

**Authors:**
Arti Vaish,
Harish Parthasarathy

**Abstract:**

**Keywords:**
Electromagnetism,
Maxwell's Equations,
Anisotropic permittivity,
Wave equation,
Matrix Equation,
Permittivity tensor.

##### 1479 Numerical Solution of Linear Ordinary Differential Equations in Quantum Chemistry by Clenshaw Method

**Authors:**
M. Saravi,
F. Ashrafi,
S.R. Mirrajei

**Abstract:**

**Keywords:**
Chebyshev polynomials,
Clenshaw method,
ODEs,
Spectral methods

##### 1478 Soliton Interaction in Multi-Core Optical Fiber: Application to WDM System

**Authors:**
S. Arun Prakash,
V. Malathi,
M. S. Mani Rajan

**Abstract:**

**Keywords:**
Optical soliton,
soliton interaction,
soliton switching,
WDM.

##### 1477 On the Integer Solutions of the Pell Equation x2 - dy2 = 2t

**Authors:**
Ahmet Tekcan,
Betül Gezer,
Osman Bizim

**Abstract:**

Let k ≥ 1 and t ≥ 0 be two integers and let d = k2 + k be a positive non-square integer. In this paper, we consider the integer solutions of Pell equation x2 - dy2 = 2t. Further we derive a recurrence relation on the solutions of this equation.

**Keywords:**
Pell equation,
Diophantine equation.

##### 1476 Mathematical Modelling of Transport Phenomena in Radioactive Waste-Cement-Bentonite Matrix

**Authors:**
Ilija Plecas,
Uranija Kozmidis-Luburic,
Radojica Pesic

**Abstract:**

The leaching rate of 137Cs from spent mix bead (anion and cation) exchange resins in a cement-bentonite matrix has been studied. Transport phenomena involved in the leaching of a radioactive material from a cement-bentonite matrix are investigated using three methods based on theoretical equations. These are: the diffusion equation for a plane source an equation for diffusion coupled to a firstorder equation and an empirical method employing a polynomial equation. The results presented in this paper are from a 25-year mortar and concrete testing project that will influence the design choices for radioactive waste packaging for a future Serbian radioactive waste disposal center.

**Keywords:**
bentonite,
cement ,
radioactive waste,
composite,
disposal,
diffusion

##### 1475 Dust Acoustic Shock Waves in Coupled Dusty Plasmas with Kappa-Distributed Ions

**Authors:**
Hamid Reza Pakzad

**Abstract:**

We have considered an unmagnetized dusty plasma system consisting of ions obeying superthermal distribution and strongly coupled negatively charged dust. We have used reductive perturbation method and derived the Kordeweg-de Vries-Burgers (KdV-Burgers) equation. The behavior of the shock waves in the plasma has been investigated.

**Keywords:**
Shock,
Soliton,
Coupling,
Superthermal ions.

##### 1474 The Proof of Two Conjectures Related to Pell-s Equation x2 −Dy2 = ± 4

**Authors:**
Armend Sh. Shabani

**Abstract:**

**Keywords:**
Pell's equation,
solutions of Pell's equation.

##### 1473 DQ Analysis of 3D Natural Convection in an Inclined Cavity Using an Velocity-Vorticity Formulation

**Abstract:**

In this paper, the differential quadrature method is applied to simulate natural convection in an inclined cubic cavity using velocity-vorticity formulation. The numerical capability of the present algorithm is demonstrated by application to natural convection in an inclined cubic cavity. The velocity Poisson equations, the vorticity transport equations and the energy equation are all solved as a coupled system of equations for the seven field variables consisting of three velocities, three vorticities and temperature. The coupled equations are simultaneously solved by imposing the vorticity definition at boundary without requiring the explicit specification of the vorticity boundary conditions. Test results obtained for an inclined cubic cavity with different angle of inclinations for Rayleigh number equal to 103, 104, 105 and 106 indicate that the present coupled solution algorithm could predict the benchmark results for temperature and flow fields. Thus, it is convinced that the present formulation is capable of solving coupled Navier-Stokes equations effectively and accurately.

**Keywords:**
Natural convection,
velocity-vorticity formulation,
differential quadrature (DQ).

##### 1472 An Analytical Method for Solving General Riccati Equation

**Authors:**
Y. Pala,
M. O. Ertas

**Abstract:**

In this paper, the general Riccati equation is analytically solved by a new transformation. By the method developed, looking at the transformed equation, whether or not an explicit solution can be obtained is readily determined. Since the present method does not require a proper solution for the general solution, it is especially suitable for equations whose proper solutions cannot be seen at first glance. Since the transformed second order linear equation obtained by the present transformation has the simplest form that it can have, it is immediately seen whether or not the original equation can be solved analytically. The present method is exemplified by several examples.

**Keywords:**
Riccati Equation,
ordinary differential equation,
nonlinear differential equation,
analytical solution,
proper solution.

##### 1471 The Pell Equation x2 − Py2 = Q

**Authors:**
Ahmet Tekcan,
Arzu Özkoç,
Canan Kocapınar,
Hatice Alkan

**Abstract:**

**Keywords:**
Pell equation,
solutions of Pell equation.

##### 1470 The Diophantine Equation y2 − 2yx − 3 = 0 and Corresponding Curves over Fp

**Authors:**
Ahmet Tekcan,
Arzu Özkoç,
Hatice Alkan

**Abstract:**

**Keywords:**
Diophantine equation,
Pell equation,
quadratic form.

##### 1469 Equations of Pulse Propagation in Three-Layer Structure of As2S3 Chalcogenide Plasmonic Nano-Waveguides

**Authors:**
Leila Motamed-Jahromi,
Mohsen Hatami,
Alireza Keshavarz

**Abstract:**

This research aims at obtaining the equations of pulse propagation in nonlinear plasmonic waveguides created with As_{2}S_{3} chalcogenide materials. Via utilizing Helmholtz equation and first-order perturbation theory, two components of electric field are determined within frequency domain. Afterwards, the equations are formulated in time domain. The obtained equations include two coupled differential equations that considers nonlinear dispersion.

**Keywords:**
Nonlinear optics,
propagation equation,
plasmonic waveguide.

##### 1468 Solution of The KdV Equation with Asymptotic Degeneracy

**Authors:**
Tapas Kumar Sinha,
Joseph Mathew

**Abstract:**

Recently T. C. Au-Yeung, C.Au, and P. C. W. Fung [2] have given the solution of the KdV equation [1] to the boundary condition , where b is a constant. We have further extended the method of [2] to find the solution of the KdV equation with asymptotic degeneracy. Via simulations we find both bright and dark Solitons (i.e. Solitons with opposite phases).

**Keywords:**
KdV equation,
Asymptotic Degeneracy,
Solitons,
Inverse Scattering

##### 1467 Exact Solutions of the Helmholtz equation via the Nikiforov-Uvarov Method

**Authors:**
Said Laachir,
Aziz Laaribi

**Abstract:**

The Helmholtz equation often arises in the study of physical problems involving partial differential equation. Many researchers have proposed numerous methods to find the analytic or approximate solutions for the proposed problems. In this work, the exact analytical solutions of the Helmholtz equation in spherical polar coordinates are presented using the Nikiforov-Uvarov (NU) method. It is found that the solution of the angular eigenfunction can be expressed by the associated-Legendre polynomial and radial eigenfunctions are obtained in terms of the Laguerre polynomials. The special case for k=0, which corresponds to the Laplace equation is also presented.

**Keywords:**
Helmholtz equation,
Nikiforov-Uvarov method,
exact solutions,
eigenfunctions.

##### 1466 Study of Cahn-Hilliard Equation to Simulate Phase Separation

**Authors:**
Nara Guimarães,
Marcelo Aquino Martorano,
Douglas Gouvêa

**Abstract:**

An investigation into Cahn-Hilliard equation was carried out through numerical simulation to identify a possible phase separation for one and two dimensional domains. It was observed that this equation can reproduce important mass fluxes necessary for phase separation within the miscibility gap and for coalescence of particles.

**Keywords:**
Cahn-Hilliard equation,
miscibility gap,
phase
separation.