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1
Publication available in full text mode
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Exact Travelling Wave Solutions to the (3+1)-Dimensional Kadomtsev-Petviashvili Equation

100%
Peng Y., Krishnan E.
Acta Physica Polonica A
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2005
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vol. 108
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issue 3
421-428
EN
Exact travelling wave solutions in terms of the Jacobi elliptic functions are obtained to the (3+1)-dimensional Kadomtsev-Petviashvili equation by means of the extended mapping method. Limit cases are studied, and new solitary wave solutions and trigonometric periodic wave solutions are got. The method is applicable to a large variety of nonlinear partial differential equations.
2
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Exact Periodic Wave Solutions to the Nizhnik-Novikov-Veselov Equation

100%
Peng Y.
Acta Physica Polonica A
|
2004
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vol. 105
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issue 5
417-424
EN
Exact periodic wave solutions to the Nizhnik-Novikov-Veselov equation are obtained by means of the modified mapping method. Limit cases are studied and new solitary wave solutions and trigonometric periodic wave solutions are found.
3
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Exact Periodic Wave Solutions of Two Types of Modified Boussinesq Equations

100%
Peng Y.
Acta Physica Polonica A
|
2003
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vol. 103
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issue 5
417-421
EN
Exact periodic wave solutions to two types of modified Boussinesq equations are obtained by the use of the Jacobi elliptic function method in a unified form. Some new, general solitary wave solutions are presented.
4
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The Variable Separation Method and Exact Jacobi Elliptic Function Solutions for the Nizhnik-Novikov-Veselov Equation

100%
Peng Y.
Acta Physica Polonica A
|
2006
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vol. 110
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issue 1
3-9
EN
Based on the singular structure analysis, the variable separation method is proposed for the Nizhnik-Novikov-Veselov equation to obtain a general functional separation solution containing three arbitrary functions. Choosing these arbitrary functions to be the Jacobi elliptic functions, a diversity of elliptic function solutions may be obtained for the equation of interest. The interaction property of the waves is numerically studied. The long wave limit gives the new type of localized coherent structures.
5
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Solitons and Other Solutions to Perturbed Rosenau-KdV-RLW Equation with Power Law Nonlinearity

63%
Sanchez P., Ebadi G., Mojaver A., Mirzazadeh M., Eslami M., Biswas A.
Acta Physica Polonica A
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2015
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vol. 127
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issue 6
1577-1587
EN
This paper obtains solitons and other solutions to the perturbed Rosenau-KdV-RLW equation that is used to model dispersive shallow water waves. This equation is taken with power law nonlinearity in this paper. There are several integration tools that are adopted to solve this equation. These are Kudryashov method, sine-cosine function method, G'/G-expansion scheme and finally the exp-function approach. Solitons and other solutions are obtained along with several constraint conditions that naturally emerge from the structure of these solutions.
6
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Applications of a Generalized Extended (G'/G) -Expansion Method to Find Exact Solutions of Two Nonlinear Schrödinger Equations with Variable Coefficients

51%
Zayed E., Abdelaziz M.
Acta Physica Polonica A
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2012
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vol. 121
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issue 3
573-580
EN
In the present paper, we construct the travelling wave solutions of two nonlinear Schrödinger equations with variable coefficients by using a generalized extended (G'/G) -expansion method, where G = G(ξ) satisfies a second order linear ordinary differential equation. By using this method, new exact solutions involving parameters, expressed by hyperbolic and trigonometric function solutions are obtained. When the parameters are taken as special values, some solitary wave solutions are derived from the hyperbolic function solutions.
7
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Application of Tanh Method to Complex Coupled Nonlinear Evolution Equations

51%
Abdelkawy M., Bhrawy A., Zerrad E., Biswas A.
Acta Physica Polonica A
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2016
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vol. 129
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issue 3
278-283
EN
This paper studies the application of tanh method to address a few coupled nonlinear evolution equations that are in complex domain. There are soliton solutions as well as triangular solutions that are revealed with this integration scheme. The equations studied in this paper are applicable to various branches of applied and theoretical physics.
8
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Numerical Solution of Fractional Black-Scholes Equation by Using the Multivariate Padé Approximation

51%
Özdemir N., Yavuz M.
Acta Physica Polonica A
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2017
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vol. 132
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issue 3
1050-1053
EN
In this study, a new application of multivariate Padé approximation method has been used for solving European vanilla call option pricing problem. Padé polynomials have occurred for the fractional Black-Scholes equation, according to the relations of "smaller than", or "greater than", between stock price and exercise price of the option. Using these polynomials, we have applied the multivariate Padé approximation method to our fractional equation and we have calculated numerical solutions of fractional Black-Scholes equation for both of two situations. The obtained results show that the multivariate Padé approximation is a very quick and accurate method for fractional Black-Scholes equation. The fractional derivative is understood in the Caputo sense.
9
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Analytical Solutions of Excited Vibrations of a Beam with Application of Distribution

51%
Kozień M.
Acta Physica Polonica A
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2013
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vol. 123
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issue 6
1029-1033
EN
In the paper, the analytical solutions of excited vibrations of the Bernoulli-Euler type beam in general case of external loading function is analyzed. The distribution theory is applied to formulate solution when the external functions are the concentrated-force type or the concentrated-moment type. Moreover, two types of excitation in time domain, harmonic and pulsed, are considered. Due to the superposition rule which can be applied in the analyzed linear case, any combination of external loading function can be formulated. The strict analytical solutions are shown for the case of simply supported beam. Describing the external load in the form of concentrated moments makes possible the analytical simulation of the reduction of vibrations of a beam by application of the piezoelectric elements which are in practice the source of external moment-type excitation put in relatively small area of action.
10
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Klein-Gordon Formulation of X-ray Diffraction in the Laue Cas

51%
Borowski J.
Acta Physica Polonica A
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2002
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vol. 101
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issue 5
767-780
EN
The Takagi-Taupin equations, the fundamental equations for X-ray diffraction deduced from the Maxwell equations, are considered. The connection between the Takagi-Taupin equations and the Klein-Gordon equation is shown. A method of solution of these equations using external differential form formalism is proposed. The solutions for both a narrow and a wide incident beams as a function of boundary conditions is analyzed. The so-called spherical and quasi-plane waves used in the X-ray experimental methods are derived from.
11
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Simulation of Control Algorithm for Active Reduction of Transversal Vibrations of Beams by Piezoelectric Elements Based on Identification of Bending Moment

51%
Kozień M., Ścisło Ł.
Acta Physica Polonica A
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2015
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vol. 128
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issue 1A
A-56-A-61
EN
Application of piezoelectric elements to active reduction of bending vibrations of the beams is known well in the literature. During vibrations, an external excitation may vary in the time domain, including its form in the frequency domain. It should have influence on their response. The problem of proper selection of the control parameter in the control algorithm used to reduce vibrations arises. In the article, simulations of a control algorithm based on detection of bending moment are analytically tested. The solution for the transient type of vibrations are obtained by the finite difference method (FDM). Analysis for two separated natural modes was performed. The analysis shows the possibility to design a control algorithm based on detection of the bending moment.
12
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Numerical Simulations of Glide Dislocations in Persistent Slip Band

51%
Kolář M., Beneš M., Kratochvíl J., Pauš P.
Acta Physica Polonica A
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2015
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vol. 128
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issue 4
506-509
EN
For the purpose of estimation of possible inaccuracy in standard discrete dislocation dynamics simulations, we study the motion of interacting dislocations in two regimes: the standard stress control and the total strain control. For demonstration of the difference, we consider two dislocations of opposite signs, gliding in parallel slip planes in a channel of a persistent slip band. Exposed to the applied stress, the dislocations move, bow out, and form a dipole. We investigate the passing stress needed for the dislocations to escape each from other, considering the stress controlled regime and the total strain controlled regime. The motion is described by the mean curvature flow and treated by means of the direct (parametric) method. The results of numerical experiments indicate that the stress control and the total strain control provide upper and lower estimate of the passing stress, respectively, and that these two estimates differ by approximately 10%.
13
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New Exact Solutions for Boussinesq Type Equations by Using (G'/G, 1/G) and (1/G')-Expansion Methods

51%
Demiray S., Ünsal Ö., Bekir A.
Acta Physica Polonica A
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2014
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vol. 125
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issue 5
1093-1098
EN
In this paper, the (G'/G, 1/G) and (1/G')-expansion methods with the aid of Maple are used to obtain new exact traveling wave solutions of the Boussinesq equation and the system of variant Boussinesq equations. The travelling wave solutions are expressed by the hyperbolic functions, the trigonometric functions, and the rational functions. It is shown that the proposed method provides a powerful mathematical tool for solving nonlinear wave equations in mathematical physics and engineering.
14
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Soliton Solution and Conservation Law of Gear-Grimshaw Model for Shallow Water Waves

51%
Triki H., Kara A., Bhrawy A., Biswas A.
Acta Physica Polonica A
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2014
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vol. 125
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issue 5
1099-1107
EN
This paper is going to obtain the soliton solution of the Gear-Grimshaw model that describes the dynamics of two-layered shallow water waves in oceans and rivers. The topological 1-soliton solution will be obtained by the ansatz method. There are several constraint conditions that will be taken care of. This will be followed by the model with power law nonlinearity. Subsequently, the conservation laws for this model will be derived by the aid of multiplier approach from the Lie symmetry analysis. Finally, the F-expansion method will extract a few more interesting solutions to the model.
15
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Exact Solutions and Conservation Laws of the Bogoyavlenskii Equation

51%
Inc M., Hashemi M., Isa Aliyu A.
Acta Physica Polonica A
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2018
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vol. 133
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issue 5
1133-1137
EN
In this paper, the Lie symmetry analysis method is performed for a Bogoyavlenskii equation. The symmetries and exact invariant solutions for the equation are retrieved for the first time. The conservation laws of the Bogoyavlenskii equation are constructed using the conservation laws theorem introduced by Ibragimov.
16
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Lie Symmetry Reductions, Exact Solutions and Conservation Laws of the Third Order Variant Boussinesq System

51%
Yaşar E., Giresunlu İ.
Acta Physica Polonica A
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2015
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vol. 128
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issue 3
252-255
EN
The Lie group method is applied to the third order variant Boussinesq system, which arises in the modelling of the water waves. The symmetry reductions and invariant solutions are obtained with respect to Lie point symmetry generators of the underlying system. In addition, we derive conservation laws of the variant Boussinesq system.
17
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Shock Waves and Other Solutions to the Benjamin-Bona-Mahoney-Burgers Equation with Dual Power-Law Nonlinearity

51%
Wang G., Xu T., Abazari R., Jovanoski Z., Biswas A.
Acta Physica Polonica A
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2014
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vol. 126
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issue 6
1221-1225
EN
We study the hybrid Benjamin-Bona-Mahoney-Burgers equation with dual power-law nonlinearity. Three different techniques - the ansatz method, Lie-symmetry analysis and the (G'/G)-expansion method - are used to find shock wave solutions. Several constraint conditions naturally emerge that guarantee the existence of shock waves. We discuss the nature of the solutions generated by the different methods.
18
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Deformation of Two Coupled Scalar Fields with Cosmological Solution

51%
Sadeghi J., Amani A.
Acta Physica Polonica A
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2008
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vol. 113
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issue 2
677-689
EN
We study the first-order formalism for the two coupled scalar fields with the superpotential W(φ,χ). As we know, the cosmological solution crucially depends on the coupled scalar fields. Here, we deform the corresponding superpotential and obtain the solution for some cosmological parameters. Finally, we compare the deformed and non-deformed solutions with the different figures.
19
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Exact Solutions and Localized Structures for a (3+1)-Dimensional Burgers Equation

51%
Peng Y.
Acta Physica Polonica A
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2012
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vol. 122
|
issue 1
20-24
EN
A (3+1)-dimensional Burgers equation is studied by the singular manifold method. By choosing different seed solutions, auto-Bäcklund transformation, the Cole-Hopf transformation and a functional separation exact solution containing two low dimensional arbitrary functions are obtained for the equation in question. Some interesting localized coherent structures are given and their interaction properties are numerically studied. Some new nonlinear phenomena are reported.
20
Content available remote

Simulation of Dislocation Annihilation by Cross-Slip

51%
Pauš P., Beneš M., Kratochvíl J.
Acta Physica Polonica A
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2012
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vol. 122
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issue 3
509-511
EN
This contribution deals with the numerical simulation of dislocation dynamics, their interaction, merging and changes in the dislocation topology. The glide dislocations are represented by parametrically described curves moving in slip planes. The simulation model is based on the numerical solution of the dislocation motion law belonging to the class of curvature driven curve dynamics. We focus on the simulation of the cross-slip of two dislocation curves where each curve evolves in a different slip plane. The dislocations evolve, under their mutual interaction and under some external force, towards each other and at a certain time their evolution continues outside slip planes. During this evolution the dislocations merge by the cross-slip occurs. As a result, there will be two dislocations evolving in three planes, two planes, and one plane where cross-slip occurred. The goal of our work is to simulate the motion of the dislocations and to determine the conditions under which the cross-slip occurs. The simulation of the dislocation evolution and merging is performed by improved parametric approach and numerical stability is enhanced by the tangential redistribution of the discretization points.
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