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1
Content available The Variable Separation Method and Exact Jacobi Elliptic Function Solutions for the Nizhnik-Novikov-Veselov Equation
100%
Peng Y.
Acta Physica Polonica A
|
2006
|
tom 110
|
nr 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.
2
Content available Exact Periodic Wave Solutions of Two Types of Modified Boussinesq Equations
100%
Peng Y.
Acta Physica Polonica A
|
2003
|
tom 103
|
nr 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.
3
Content available Exact Travelling Wave Solutions to the (3+1)-Dimensional Kadomtsev-Petviashvili Equation
100%
Peng Y. , Krishnan E.
Acta Physica Polonica A
|
2005
|
tom 108
|
nr 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.
4
Content available Exact Periodic Wave Solutions to the Nizhnik-Novikov-Veselov Equation
100%
Peng Y.
Acta Physica Polonica A
|
2004
|
tom 105
|
nr 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.
5
Content available remote 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
|
2015
|
tom 127
|
nr 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
Content available remote Analytical Solutions of Excited Vibrations of a Beam with Application of Distribution
51%
Kozień M.
Acta Physica Polonica A
|
2013
|
tom 123
|
nr 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.
7
Content available remote A Fifth-Order Korteweg-de Vries Equation for Shallow Water with Surface Tension: Multiple Soliton Solutions
51%
Wazwaz A.
Acta Physica Polonica A
|
2016
|
tom 130
|
nr 3
679-682
EN
In this work we study a fifth-order Korteweg-de Vries equation for shallow water with surface tension derived by Dullin et al. The fifth-order Korteweg-de Vries equation, derived by using the nonlinear/non-local transformations introduced by Kodama, and the Camassa-Holm equation with linear dispersion, have very different behaviors despite being asymptotically equivalent. We use the simplified form of the Hirota direct method to derive multiple soliton solutions for this equation.
8
Content available remote 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.
|
|
nr 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.
9
Content available remote Some Exact and Explicit Solutions for Nonlinear Schrödinger Equations
51%
Aslan İ.
Acta Physica Polonica A
|
2013
|
tom 123
|
nr 1
16-20
EN
Nonlinear models occur in many areas of applied physical sciences. This paper presents the first integral method to carry out the integration of Schrödinger-type equations in terms of traveling wave solutions. Through the established first integrals, exact traveling wave solutions are obtained under some parameter conditions.
10
Content available remote Self-Ordered Front under Temporally Irregular Forcing: Ratchet-Like Transport of the Quasi-Periodically Forced Front
51%
Bakanas R. , Ivanauskas F. , Jasaitis V.
Acta Physica Polonica A
|
2011
|
tom 119
|
nr 6
731-739
EN
Ratchet-like transport of the quasi-periodically forced "bistable" front joining two states of the different stability in the reaction-diffusion system is considered by use of the piecewise linear rate (reaction) function of the reaction kinetics. We approximate the oscillatory force acting on the front in the system by the bi-harmonic forcing functions being a superposition of the single-harmonic components (the Fourier modes) of the different frequencies, either commensurate or incommensurable ones. By considering the response of the self-ordered front to the oscillatory forces used we analyze the effect of the temporally irregular oscillations of the ac forcing on the ratchet-like shuttling of the ac driven front. By comparing the average characteristics of the spurious drift derivable in both cases of the periodically and quasi-periodically forced fronts we show that the temporally irregular fluctuations of the oscillatory force shrink the spurious drift of the front. More specifically, we find the performance of the ratchet-like shuttling of the self-ordered fronts is much lesser pronounced with the quasi-periodic, temporally irregular ac forcing if compared to that derivable by the rigorously periodic forcing, in both cases of the symmetrical and asymmetrical rate functions satisfying the different symmetry. The average characteristics of the spurious drift, that describe the dependence of the mean drift velocity of the ac driven front versus both the amplitude (strength) and the frequency of the oscillatory forces used are presented.
11
Content available remote 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
|
2014
|
tom 126
|
nr 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.
12
Content available remote 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
|
2014
|
tom 125
|
nr 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.
13
Content available remote 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
|
2014
|
tom 125
|
nr 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.
14
Content available remote Exact Solutions and Localized Structures for a (3+1)-Dimensional Burgers Equation
51%
Peng Y.
|
|
nr 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.
15
Content available remote Numerical Simulation of Dislocation Cross-Slip with Annihilation in Non-Symmetric Configuration
51%
Pauš P. , Beneš M. , Kratochvíl J.
Acta Physica Polonica A
|
2015
|
tom 128
|
nr 4
737-739
EN
The interpretation of the experimentally determined critical distance of the screw dislocation annihilation in persistent slip bands is still an open question. We attempt to analyze this problem using the discrete dislocation dynamics simulations. Dislocations are represented by parametrically described curves. The 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 one edge dislocation curve bowing out of the wall of a persistent slip band channel and one screw dislocation gliding through the channel. The dislocations move under their mutual interaction, the line tension and the applied stress. A cross-slip leads to annihilation of the dipolar parts. In the changed topology each dislocation evolves in two slip planes and the plane where cross-slip occurred. The goal of our work is to develop and test suitable mathematical and physical model of the situation. The results are subject to comparison with symmetric configuration of two screw dislocations studied in papers by Pauš et al. The simulation of the dislocation evolution and merging is performed by the improved parametric approach. Numerical stability is enhanced by the tangential redistribution of the discretization points.
16
Content available remote Numerical Simulations of Glide Dislocations in Persistent Slip Band
51%
Kolář M. , Beneš M. , Kratochvíl J. , Pauš P.
Acta Physica Polonica A
|
2015
|
tom 128
|
nr 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%.
17
Content available remote Simulation of Dislocation Annihilation by Cross-Slip
51%
Pauš P. , Beneš M. , Kratochvíl J.
|
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.
18
Content available remote Front Dynamics with Time Delays in a Bistable System of the Reaction-Diffusion Type: Role of the Symmetry of the Rate Function
51%
Bakanas R. , Ivanauskas F. , Jasaitis V.
Acta Physica Polonica A
|
2011
|
tom 119
|
nr 3
282-297
EN
The retardation effects in dynamics of the ac driven "bistable" fronts joining two states of the different stability in a bistable system of the reaction-diffusion type are investigated by use of the macroscopic kinetic equation of the reaction kinetics. We approximate the rate (reaction) function in the governing equation of "bistable" fronts by the piecewise linear dependence of the flexible symmetry, encompassing both cases of the symmetrical and asymmetrical rate functions. By numerically simulating the drift motion of the ac driven front being subjected to the time-dependent step-like (rectangular) forcing we investigate the lag time between the ac force and the instantaneous velocity of the ac driven front. We find that the time lags derivable by the symmetrical and asymmetrical rate functions notably differ, namely, we show that (a) the lag time is a function of the outer slope coefficients of the rate function and is not sensitive to the inner, (b) it has only weak dependence on the strength of the applied forcing, (c) the retardation effects (time lags) in the front dynamics are describable adequately enough by use of the perturbation theory. Another aspect of the front dynamics discussed in this report is the influence of the retardation effects on the ratchet-like transport of the ac driven fronts being described by the asymmetrical rate functions of the "low" symmetry. By considering the response of "bistable" front to the single-harmonic ac force we find that the occurrence of the time lags in the oscillatory motion of the ac driven front shrink the spurious drift of the front; the spurious drift practically disappears if the frequency of the oscillatory force significantly exceeds the characteristic relaxation rate of the system. Furthermore, the occurrence of the time lags in the front dynamics leads to the vanishing of the reversals in the directed net motion of the ac driven fronts, being always inherent in the case of the slow (quasi-stationary) ac drive, i.e., the possibilities of controlling the directed net motion of the self-ordered fronts by the low- and high-frequency zero-mean ac forces radically differ.
19
Content available remote Exact Solutions of Bose-Einstein Condensate in Linear Magnetic Field and Time-Dependent Laser Field
51%
Huang W. , Mao J. , Qiu W.
Acta Physica Polonica A
|
2011
|
tom 119
|
nr 3
294-297
EN
A generalized G'/G-expansion method is extended to construct exact solutions for the Gross-Pitaevskii equation with weak bias magnetic and time-dependent laser fields. Many types of exact solutions including hyperbolic function solution, trigonometric function solution and rational exact solution with parameters are obtained. In addition, soliton solutions are found.
20
Content available remote Numerical Solution of Fractional Black-Scholes Equation by Using the Multivariate Padé Approximation
51%
Özdemir N. , Yavuz M.
Acta Physica Polonica A
|
2017
|
tom 132
|
nr 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.
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