**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**1536

# Search results for: Schrödinger wave equation.

##### 1536 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.

##### 1535 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.

##### 1534 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

##### 1533 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.

##### 1532 Traveling Wave Solutions for Shallow Water Wave Equation by (G'/G)-Expansion Method

**Authors:**
Anjali Verma,
Ram Jiwari,
Jitender Kumar

**Abstract:**

This paper presents a new function expansion method for finding traveling wave solution of a non-linear equation and calls it the (G'/G)-expansion method. The shallow water wave equation is reduced to a non linear ordinary differential equation by using a simple transformation. As a result the traveling wave solutions of shallow water wave equation are expressed in three forms: hyperbolic solutions, trigonometric solutions and rational solutions.

**Keywords:**
Shallow water wave equation,
Exact solutions,
(G'/G) expansion method.

##### 1531 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.

##### 1530 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

##### 1529 Extend Three-wave Method for the (3+1)-Dimensional Soliton Equation

**Authors:**
Somayeh Arbabi Mohammad-Abadi,
Maliheh Najafi

**Abstract:**

In this paper, we study (3+1)-dimensional Soliton equation. We employ the Hirota-s bilinear method to obtain the bilinear form of (3+1)-dimensional Soliton equation. Then by the idea of extended three-wave method, some exact soliton solutions including breather type solutions are presented.

**Keywords:**
Three-wave method,
(3+1)-dimensional Soliton equation,
Hirota's bilinear form.

##### 1528 On Symmetry Analysis and Exact Wave Solutions of New Modified Novikov Equation

**Authors:**
Anupma Bansal,
R. K. Gupta

**Abstract:**

In this paper, we study a new modified Novikov equation for its classical and nonclassical symmetries and use the symmetries to reduce it to a nonlinear ordinary differential equation (ODE). With the aid of solutions of the nonlinear ODE by using the modified (G/G)-expansion method proposed recently, multiple exact traveling wave solutions are obtained and the traveling wave solutions are expressed by the hyperbolic functions, trigonometric functions and rational functions.

**Keywords:**
New Modified Novikov Equation,
Lie Classical Method,
Nonclassical Method,
Modified (G'/G)-Expansion Method,
Traveling Wave Solutions.

##### 1527 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.

##### 1526 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

##### 1525 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

##### 1524 Solving Inhomogeneous Wave Equation Cauchy Problems using Homotopy Perturbation Method

**Authors:**
Mohamed M. Mousa,
Aidarkhan Kaltayev

**Abstract:**

In this paper, He-s homotopy perturbation method (HPM) is applied to spatial one and three spatial dimensional inhomogeneous wave equation Cauchy problems for obtaining exact solutions. HPM is used for analytic handling of these equations. The results reveal that the HPM is a very effective, convenient and quite accurate to such types of partial differential equations (PDEs).

**Keywords:**
Homotopy perturbation method,
Exact solution,
Cauchy problem,
inhomogeneous wave equation

##### 1523 The Direct Ansaz Method for Finding Exact Multi-Wave Solutions to the (2+1)-Dimensional Extension of the Korteweg de-Vries Equation

**Authors:**
Chuanjian Wang,
Changfu Liu,
Zhengde Dai

**Abstract:**

In this paper, the direct AnsAz method is used for constructing the multi-wave solutions to the (2+1)-dimensional extension of the Korteweg de-Vries (shortly EKdV) equation. A new breather type of three-wave solutions including periodic breather type soliton solution, breather type of two-solitary solution are obtained. Some cases with specific values of the involved parameters are plotted for each of the three-wave solutions. Mechanical features of resonance interaction among the multi-wave are discussed. These results enrich the variety of the dynamics of higher-dimensional nonlinear wave field.

**Keywords:**
EKdV equation,
Breather,
Soliton,
Bilinear form,
The
direct AnsAz method.

##### 1522 Traveling Wave Solutions for the Sawada-Kotera-Kadomtsev-Petviashivili Equation and the Bogoyavlensky-Konoplechenko Equation by (G'/G)- Expansion Method

**Authors:**
Nisha Goyal,
R.K. Gupta

**Abstract:**

This paper presents a new function expansion method for finding traveling wave solutions of a nonlinear equations and calls it the G G -expansion method, given by Wang et al recently. As an application of this new method, we study the well-known Sawada-Kotera-Kadomtsev-Petviashivili equation and Bogoyavlensky-Konoplechenko equation. With two new expansions, general types of soliton solutions and periodic solutions for these two equations are obtained.

**Keywords:**
Sawada-Kotera-Kadomtsev-Petviashivili equation,
Bogoyavlensky-Konoplechenko equation,

##### 1521 Cubic Trigonometric B-spline Approach to Numerical Solution of Wave Equation

**Authors:**
Shazalina Mat Zin,
Ahmad Abd. Majid,
Ahmad Izani Md. Ismail,
Muhammad Abbas

**Abstract:**

The generalized wave equation models various problems in sciences and engineering. In this paper, a new three-time level implicit approach based on cubic trigonometric B-spline for the approximate solution of wave equation is developed. The usual finite difference approach is used to discretize the time derivative while cubic trigonometric B-spline is applied as an interpolating function in the space dimension. Von Neumann stability analysis is used to analyze the proposed method. Two problems are discussed to exhibit the feasibility and capability of the method. The absolute errors and maximum error are computed to assess the performance of the proposed method. The results were found to be in good agreement with known solutions and with existing schemes in literature.

**Keywords:**
Collocation method,
Cubic trigonometric B-spline,
Finite difference,
Wave equation.

##### 1520 Investigation of Stoneley Waves in Multilayered Plates

**Authors:**
Bing Li,
Tong Lu,
Lei Qiang

**Abstract:**

Stoneley waves are interface waves that propagate at the interface between two solid media. In this study, the dispersion characteristics and wave structures of Stoneley waves in elastic multilayered plates are displayed and investigated. With a perspective of bulk wave, a reasonable assumption of the potential function forms of the expansion wave and shear wave in *n*th layer medium is adopted, and the characteristic equation of Stoneley waves in a three-layered plate is given in a determinant form. The dispersion curves and wave structures are solved and presented in both numerical and simulation results. It is observed that two Stoneley wave modes exist in a three-layered plate, that conspicuous dispersion occurs on low frequency band, that the velocity of each Stoneley wave mode approaches the corresponding Stoneley wave velocity at interface between two half infinite spaces. The wave structures reveal that the in-plane displacement of Stoneley waves are relatively high at interfaces, which shows great potential for interface defects detection.

**Keywords:**
Characteristic equation,
interface waves,
dispersion curves,
potential function,
Stoneley waves,
wave structures.

##### 1519 Solitary Wave Solutions for Burgers-Fisher type Equations with Variable Coefficients

**Authors:**
Amit Goyal,
Alka,
Rama Gupta,
C. Nagaraja Kumar

**Abstract:**

**Keywords:**
Solitary wave solution,
Variable coefficient Burgers-
Fisher equation,
Auxiliary equation method.

##### 1518 The Splitting Upwind Schemes for Spectral Action Balance Equation

**Authors:**
Anirut Luadsong,
Nitima Aschariyaphotha

**Abstract:**

**Keywords:**
upwind scheme,
parallel algorithm,
spectral action balance equation,
splitting method.

##### 1517 Some Exact Solutions of the (2+1)-Dimensional Breaking Soliton Equation using the Three-wave Method

**Authors:**
Mohammad Taghi Darvishi,
Mohammad Najafi

**Abstract:**

This paper considers the (2+1)-dimensional breaking soliton equation in its bilinear form. Some exact solutions to this equation are explicitly derived by the idea of three-wave solution method with the assistance of Maple. We can see that the new idea is very simple and straightforward.

**Keywords:**
Soliton solution,
computerized symbolic computation,
painleve analysis,
(2+1)-dimensional breaking soliton equation,
Hirota's bilinear form.

##### 1516 Traveling Wave Solutions for the (3+1)-Dimensional Breaking Soliton Equation by (G'/G)- Expansion Method and Modified F-Expansion Method

**Authors:**
Mohammad Taghi Darvishi,
Maliheh Najafi,
Mohammad Najafi

**Abstract:**

In this paper, using (G/G )-expansion method and modified F-expansion method, we give some explicit formulas of exact traveling wave solutions for the (3+1)-dimensional breaking soliton equation. A modified F-expansion method is proposed by taking full advantages of F-expansion method and Riccati equation in seeking exact solutions of the equation.

**Keywords:**
Exact solution,
The (3+1)-dimensional breaking soliton equation,
( G G )-expansion method,
Riccati equation,
Modified Fexpansion method.

##### 1515 Fourier Galerkin Approach to Wave Equation with Absorbing Boundary Conditions

**Authors:**
Alexandra Leukauf,
Alexander Schirrer,
Emir Talic

**Abstract:**

**Keywords:**
Absorbing boundary conditions,
boundary control,
Fourier Galerkin approach,
modal approach,
wave equation.

##### 1514 Splitting Modified Donor-Cell Schemes for Spectral Action Balance Equation

**Authors:**
Tanapat Brikshavana,
Anirut Luadsong

**Abstract:**

**Keywords:**
donor-cell scheme,
parallel algorithm,
spectral action balance equation,
splitting method.

##### 1513 Analytical Investigation of the Effects of a Standing Ocean Wave in a Wave-Power Device OWC

**Authors:**
E.G. Bautista,
F. Méndez,
O. Bautista,
J.C. Arcos

**Abstract:**

**Keywords:**
Oscillating water column,
Shallow flow,
Waveenergy.

##### 1512 Simulation of Irregular Waves by CFD

**Authors:**
Muniyandy Elangovan

**Abstract:**

**Keywords:**
Numerical wave tank,
irregular wave,
FFT,
wavespectrum

##### 1511 Alternating Implicit Block FDTD Method For Scalar Wave Equation

**Authors:**
N. M. Nusi,
M. Othman,
M. Suleiman,
F. Ismail,
N. Alias

**Abstract:**

**Keywords:**
FDTD,
Scalar wave equation,
alternating direction
implicit (ADI),
alternating group explicit (AGE),
asymmetric approximation.

##### 1510 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.

##### 1509 Stress Solitary Waves Generated by a Second-Order Polynomial Constitutive Equation

**Authors:**
Tsun-Hui Huang,
Shyue-Cheng Yang,
Chiou-Fen Shieh

**Abstract:**

In this paper, a nonlinear constitutive law and a curve fitting, two relationships between the stress-strain and the shear stress-strain for sandstone material were used to obtain a second-order polynomial constitutive equation. Based on the established polynomial constitutive equations and Newton’s second law, a mathematical model of the non-homogeneous nonlinear wave equation under an external pressure was derived. The external pressure can be assumed as an impulse function to simulate a real earthquake source. A displacement response under nonlinear two-dimensional wave equation was determined by a numerical method and computer-aided software. The results show that a suit pressure in the sandstone generates the phenomenon of stress solitary waves.

**Keywords:**
Polynomial constitutive equation,
solitary.

##### 1508 Nonlinear Effects in Bubbly Liquid with Shock Waves

**Authors:**
Raisa Kh. Bolotnova,
Marat N. Galimzianov,
Andrey S. Topolnikov,
Uliana O. Agisheva,
Valeria A. Buzina

**Abstract:**

**Keywords:**
bubbly liquid,
cavitation,
equation of state,
shock
wave

##### 1507 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.