Exact solutions in three-dimensional gravity

CERN Document Server

Garcia-Diaz, Alberto A

2017-01-01

A self-contained text, systematically presenting the determination and classification of exact solutions in three-dimensional Einstein gravity. This book explores the theoretical framework and general physical and geometrical characteristics of each class of solutions, and includes information on the researchers responsible for their discovery. Beginning with the physical character of the solutions, these are identified and ordered on the basis of their geometrical invariant properties, symmetries, and algebraic classifications, or from the standpoint of their physical nature, for example electrodynamic fields, fluid, scalar field, or dilaton. Consequently, this text serves as a thorough catalogue on 2+1 exact solutions to the Einstein equations coupled to matter and fields, and on vacuum solutions of topologically massive gravity with a cosmological constant. The solutions are also examined from different perspectives, enabling a conceptual bridge between exact solutions of three- and four-dimensional gravit...

New exact solutions of the mBBM equation

International Nuclear Information System (INIS)

Zhang Zhe; Li Desheng

2013-01-01

The enhanced modified simple equation method presented in this article is applied to construct the exact solutions of modified Benjamin-Bona-Mahoney equation. Some new exact solutions are derived by using this method. When some parameters are taken as special values, the solitary wave solutions can be got from the exact solutions. It is shown that the method introduced in this paper has general significance in searching for exact solutions to the nonlinear evolution equations. (authors)

Quasi exactly solvable operators and abstract associative algebras

International Nuclear Information System (INIS)

Brihaye, Y.; Kosinski, P.

1998-01-01

We consider the vector spaces consisting of direct sums of polynomials of given degrees and we show how to classify the linear differential operators preserving these spaces. The families of operators so obtained are identified as the envelopping algebras of particular abstract associative algebras. Some of these operators can be transformed into quasi exactly solvable Schroedinger operators which, having a hidden algebra, can be partially solved algebraically; we exhibit however a series of Schoedinger equations which, while completely solvable algebraically, do not possess a hidden algebra

Classes of exact Einstein Maxwell solutions

Science.gov (United States)

Komathiraj, K.; Maharaj, S. D.

2007-12-01

We find new classes of exact solutions to the Einstein Maxwell system of equations for a charged sphere with a particular choice of the electric field intensity and one of the gravitational potentials. The condition of pressure isotropy is reduced to a linear, second order differential equation which can be solved in general. Consequently we can find exact solutions to the Einstein Maxwell field equations corresponding to a static spherically symmetric gravitational potential in terms of hypergeometric functions. It is possible to find exact solutions which can be written explicitly in terms of elementary functions, namely polynomials and product of polynomials and algebraic functions. Uncharged solutions are regainable with our choice of electric field intensity; in particular we generate the Einstein universe for particular parameter values.

Exact solutions, numerical relativity and gravitational radiation

International Nuclear Information System (INIS)

Winicour, J.

1986-01-01

In recent years, there has emerged a new use for exact solutions to Einstein's equation as checks on the accuracy of numerical relativity codes. Much has already been written about codes based upon the space-like Cauchy problem. In the case of two Killing vectors, a numerical characteristic initial value formulation based upon two intersecting families of null hypersurfaces has successfully evolved the Schwarzschild and the colliding plane wave vacuum solutions. Here the author discusses, in the context of exact solutions, numerical studies of gravitational radiation based upon the null cone initial value problem. Every stage of progress in the null cone approach has been associated with exact solutions in some sense. He begins by briefly recapping this history. Then he presents two new examples illustrating how exact solutions can be useful

New quasi-exactly solvable Hermitian as well as non-Hermitian PT ...

Indian Academy of Sciences (India)

Abstract. We start with quasi-exactly solvable (QES) Hermitian (and hence real) as ... the time reversal transformation t → −t and further, one replaces i → −i. One can ..... F M Fernandez, R Guardiola, J Ros and M Znojil, J. Phys. A32, 3105 ...

Perturbation of an exact strong gravity solution

International Nuclear Information System (INIS)

Baran, S.A.

1982-10-01

Perturbations of an exact strong gravity solution are investigated. It is shown, by using the new multipole expansions previously presented, that this exact and static spherically symmetric solution is stable under odd parity perturbations. (author)

New quasi-exactly solvable Hermitian as well as non-Hermitian PT ...

Indian Academy of Sciences (India)

We start with quasi-exactly solvable (QES) Hermitian (and hence real) as well as complex P T -invariant, double sinh-Gordon potential and show that even after adding perturbation terms, the resulting potentials, in both cases, are still QES potentials. Further, by using anti-isospectral transformations, we obtain Hermitian as ...

Exact harmonic solutions to Guyer-Krumhansl-type equation and application to heat transport in thin films

Science.gov (United States)

Zhukovsky, K.; Oskolkov, D.

2018-03-01

A system of hyperbolic-type inhomogeneous differential equations (DE) is considered for non-Fourier heat transfer in thin films. Exact harmonic solutions to Guyer-Krumhansl-type heat equation and to the system of inhomogeneous DE are obtained in Cauchy- and Dirichlet-type conditions. The contribution of the ballistic-type heat transport, of the Cattaneo heat waves and of the Fourier heat diffusion is discussed and compared with each other in various conditions. The application of the study to the ballistic heat transport in thin films is performed. Rapid evolution of the ballistic quasi-temperature component in low-dimensional systems is elucidated and compared with slow evolution of its diffusive counterpart. The effect of the ballistic quasi-temperature component on the evolution of the complete quasi-temperature is explored. In this context, the influence of the Knudsen number and of Cauchy- and Dirichlet-type conditions on the evolution of the temperature distribution is explored. The comparative analysis of the obtained solutions is performed.

Extremal black holes as exact string solutions

International Nuclear Information System (INIS)

Horowitz, G.T.; Tseytlin, A.A.

1994-01-01

We show that the leading order solution describing an extremal electrically charged black hole in string theory is, in fact, an exact solution to all orders in α' when interpreted in a Kaluza-Klein fashion. This follows from the observation that it can be obtained via dimensional reduction from a five-dimensional background which is proved to be an exact string solution

Quasi-exact evaluation of time domain MFIE MOT matrix elements

KAUST Repository

Shi, Yifei; Bagci, Hakan; Shanker, Balasubramaniam; Lu, Mingyu; Michielssen, Eric

2013-01-01

A previously proposed quasi-exact scheme for evaluating matrix elements resulting from the marching-on-in-time (MOT) discretization of the time domain electric field integral equation (EFIE) is extended to matrix entries resulting from the discretization of its magnetic field integral equation (MFIE) counterpart. Numerical results demonstrate the accuracy of the scheme as well as the late-time stability of the resulting MOT-MFIE solver. © 2013 IEEE.

Quasi-exact evaluation of time domain MFIE MOT matrix elements

KAUST Repository

Shi, Yifei

2013-07-01

A previously proposed quasi-exact scheme for evaluating matrix elements resulting from the marching-on-in-time (MOT) discretization of the time domain electric field integral equation (EFIE) is extended to matrix entries resulting from the discretization of its magnetic field integral equation (MFIE) counterpart. Numerical results demonstrate the accuracy of the scheme as well as the late-time stability of the resulting MOT-MFIE solver. © 2013 IEEE.

Exact solution of the hidden Markov processes

Science.gov (United States)

Saakian, David B.

2017-11-01

We write a master equation for the distributions related to hidden Markov processes (HMPs) and solve it using a functional equation. Thus the solution of HMPs is mapped exactly to the solution of the functional equation. For a general case the latter can be solved only numerically. We derive an exact expression for the entropy of HMPs. Our expression for the entropy is an alternative to the ones given before by the solution of integral equations. The exact solution is possible because actually the model can be considered as a generalized random walk on a one-dimensional strip. While we give the solution for the two second-order matrices, our solution can be easily generalized for the L values of the Markov process and M values of observables: We should be able to solve a system of L functional equations in the space of dimension M -1 .

Polygons of differential equations for finding exact solutions

International Nuclear Information System (INIS)

Kudryashov, Nikolai A.; Demina, Maria V.

2007-01-01

A method for finding exact solutions of nonlinear differential equations is presented. Our method is based on the application of polygons corresponding to nonlinear differential equations. It allows one to express exact solutions of the equation studied through solutions of another equation using properties of the basic equation itself. The ideas of power geometry are used and developed. Our approach has a pictorial interpretation, which is illustrative and effective. The method can be also applied for finding transformations between solutions of differential equations. To demonstrate the method application exact solutions of several equations are found. These equations are: the Korteveg-de Vries-Burgers equation, the generalized Kuramoto-Sivashinsky equation, the fourth-order nonlinear evolution equation, the fifth-order Korteveg-de Vries equation, the fifth-order modified Korteveg-de Vries equation and the sixth-order nonlinear evolution equation describing turbulent processes. Some new exact solutions of nonlinear evolution equations are given

On exact solutions of scattering problems

International Nuclear Information System (INIS)

Nikishov, P.Yu.; Plekhanov, E.B.; Zakhariev, B.N.

1982-01-01

Examples illustrating the quality of the reconstruction of potentials from single-channel scattering data by using exactly solvable models are given. Simple exact solutions for multi-channel systems with non-degenerated resonance singularities of the scattering matrix are derived

Exact Solutions for Einstein's Hyperbolic Geometric Flow

International Nuclear Information System (INIS)

He Chunlei

2008-01-01

In this paper we investigate the Einstein's hyperbolic geometric flow and obtain some interesting exact solutions for this kind of flow. Many interesting properties of these exact solutions have also been analyzed and we believe that these properties of Einstein's hyperbolic geometric flow are very helpful to understanding the Einstein equations and the hyperbolic geometric flow

Exact solution of nonsteady thermal boundary layer equation

International Nuclear Information System (INIS)

Dorfman, A.S.

1995-01-01

There are only a few exact solutions of the thermal boundary layer equation. Most of them are derived for a specific surface temperature distribution. The first exact solution of the steady-state boundary layer equation was given for a plate with constant surface temperature and free-stream velocity. The same problem for a plate with polynomial surface temperature distribution was solved by Chapmen and Rubesin. Levy gave the exact solution for the case of a power law distribution of both surface temperature and free-stream velocity. The exact solution of the steady-state boundary layer equation for an arbitrary surface temperature and a power law free-stream velocity distribution was given by the author in two forms: of series and of the integral with an influence function of unheated zone. A similar solution of the nonsteady thermal boundary layer equation for an arbitrary surface temperature and a power law free-stream velocity distribution is presented here. In this case, the coefficients of series depend on time, and in the limit t → ∞ they become the constant coefficients of a similar solution published before. This solution, unlike the one presented here, does not satisfy the initial conditions at t = 0, and, hence, can be used only in time after the beginning of the process. The solution in the form of a series becomes a closed-form exact solution for polynomial surface temperature and a power law free-stream velocity distribution. 7 refs., 2 figs

Exact Markov chain and approximate diffusion solution for haploid genetic drift with one-way mutation.

Science.gov (United States)

Hössjer, Ola; Tyvand, Peder A; Miloh, Touvia

2016-02-01

The classical Kimura solution of the diffusion equation is investigated for a haploid random mating (Wright-Fisher) model, with one-way mutations and initial-value specified by the founder population. The validity of the transient diffusion solution is checked by exact Markov chain computations, using a Jordan decomposition of the transition matrix. The conclusion is that the one-way diffusion model mostly works well, although the rate of convergence depends on the initial allele frequency and the mutation rate. The diffusion approximation is poor for mutation rates so low that the non-fixation boundary is regular. When this happens we perturb the diffusion solution around the non-fixation boundary and obtain a more accurate approximation that takes quasi-fixation of the mutant allele into account. The main application is to quantify how fast a specific genetic variant of the infinite alleles model is lost. We also discuss extensions of the quasi-fixation approach to other models with small mutation rates. Copyright © 2015 Elsevier Inc. All rights reserved.

Exact solution for the generalized Telegraph Fisher's equation

International Nuclear Information System (INIS)

Abdusalam, H.A.; Fahmy, E.S.

2009-01-01

In this paper, we applied the factorization scheme for the generalized Telegraph Fisher's equation and an exact particular solution has been found. The exact particular solution for the generalized Fisher's equation was obtained as a particular case of the generalized Telegraph Fisher's equation and the two-parameter solution can be obtained when n=2.

New exact solutions of the Dirac equation. 11

International Nuclear Information System (INIS)

Bagrov, V.G.; Noskov, M.D.

1984-01-01

Investigations into determining new exact solutions of relativistic wave equations started in another paper were continued. Exact solutions of the Dirac, Klein-Gordon equations and classical relativistic equations of motion in four new types of external electromagnetic fields were found

Constructing exact symmetric informationally complete measurements from numerical solutions

Science.gov (United States)

Appleby, Marcus; Chien, Tuan-Yow; Flammia, Steven; Waldron, Shayne

2018-04-01

Recently, several intriguing conjectures have been proposed connecting symmetric informationally complete quantum measurements (SIC POVMs, or SICs) and algebraic number theory. These conjectures relate the SICs to their minimal defining algebraic number field. Testing or sharpening these conjectures requires that the SICs are expressed exactly, rather than as numerical approximations. While many exact solutions of SICs have been constructed previously using Gröbner bases, this method has probably been taken as far as is possible with current computer technology (except in special cases where there are additional symmetries). Here, we describe a method for converting high-precision numerical solutions into exact ones using an integer relation algorithm in conjunction with the Galois symmetries of an SIC. Using this method, we have calculated 69 new exact solutions, including nine new dimensions, where previously only numerical solutions were known—which more than triples the number of known exact solutions. In some cases, the solutions require number fields with degrees as high as 12 288. We use these solutions to confirm that they obey the number-theoretic conjectures, and address two questions suggested by the previous work.

An Exact Solution of the Binary Singular Problem

Directory of Open Access Journals (Sweden)

Baiqing Sun

2014-01-01

Full Text Available Singularity problem exists in various branches of applied mathematics. Such ordinary differential equations accompany singular coefficients. In this paper, by using the properties of reproducing kernel, the exact solution expressions of dual singular problem are given in the reproducing kernel space and studied, also for a class of singular problem. For the binary equation of singular points, I put it into the singular problem first, and then reuse some excellent properties which are applied to solve the method of solving differential equations for its exact solution expression of binary singular integral equation in reproducing kernel space, and then obtain its approximate solution through the evaluation of exact solutions. Numerical examples will show the effectiveness of this method.

Exact traveling wave solutions of the Boussinesq equation

International Nuclear Information System (INIS)

Ding Shuangshuang; Zhao Xiqiang

2006-01-01

The repeated homogeneous balance method is used to construct exact traveling wave solutions of the Boussinesq equation, in which the homogeneous balance method is applied to solve the Riccati equation and the reduced nonlinear ordinary differential equation, respectively. Many new exact traveling wave solutions of the Boussinesq equation are successfully obtained

Exact solutions in string-motivated scalar-field cosmology

International Nuclear Information System (INIS)

Oezer, M.; Taha, M.O.

1992-01-01

Two exact cosmological solutions to a scalar-field potential motivated by six-dimensional (6D) Einstein-Maxwell theory are given. The resulting pure scalar-field cosmology is free of singularity and causality problems but conserves entropy. These solutions are then extended into exact cosmological solutions for a decaying scalar field with an approximate two-loop 4D string potential. The resulting cosmology is, for both solutions, free of cosmological problems and close to the standard cosmology of the radiation era

Exact solutions of some nonlinear partial differential equations using ...

Indian Academy of Sciences (India)

The functional variable method is a powerful solution method for obtaining exact solutions of some nonlinear partial differential equations. In this paper, the functional variable method is used to establish exact solutions of the generalized forms of Klein–Gordon equation, the (2 + 1)-dimensional Camassa–Holm ...

General solution of the Dirac equation for quasi-two-dimensional electrons

Energy Technology Data Exchange (ETDEWEB)

Eremko, Alexander, E-mail: eremko@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Str., 14-b, Kyiv, 03680 (Ukraine); Brizhik, Larissa, E-mail: brizhik@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Str., 14-b, Kyiv, 03680 (Ukraine); Loktev, Vadim, E-mail: vloktev@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Str., 14-b, Kyiv, 03680 (Ukraine); National Technical University of Ukraine “KPI”, Peremohy av., 37, Kyiv, 03056 (Ukraine)

2016-06-15

The general solution of the Dirac equation for quasi-two-dimensional electrons confined in an asymmetric quantum well, is found. The energy spectrum of such a system is exactly calculated using special unitary operator and is shown to depend on the electron spin polarization. This solution contains free parameters, whose variation continuously transforms one known particular solution into another. As an example, two different cases are considered in detail: electron in a deep and in a strongly asymmetric shallow quantum well. The effective mass renormalized by relativistic corrections and Bychkov–Rashba coefficients are analytically obtained for both cases. It is demonstrated that the general solution transforms to the particular solutions, found previously (Eremko et al., 2015) with the use of spin invariants. The general solution allows to establish conditions at which a specific (accompanied or non-accompanied by Rashba splitting) spin state can be realized. These results can prompt the ways to control the spin degree of freedom via the synthesis of spintronic heterostructures with the required properties.

Symmetries and exact solutions of the nondiagonal Einstein-Rosen metrics

International Nuclear Information System (INIS)

Goyal, N; Gupta, R K

2012-01-01

We seek exact solutions of the nondiagonal Einstein-Rosen metrics. The method of Lie symmetry of differential equations is utilized to obtain new exact solutions of Einstein vacuum equations obtained from the nondiagonal Einstein-Rosen metric. Four cases arise depending on the nature of the Lie symmetry generator. In all cases, we find reductions in terms of ordinary differential equations and exact solutions of the nonlinear system of partial differential equations (PDEs) are derived. For this purpose, first we check the Painlevé property and then corresponding to the nonlinear system of PDEs, symmetries and exact solutions are obtained.

Duality and self-duality (energy reflection symmetry) of quasi-exactly solvable periodic potentials

International Nuclear Information System (INIS)

Dunne, Gerald V.; Shifman, M.

2002-01-01

A class of spectral problems with a hidden Lie-algebraic structure is considered. We define a duality transformation which maps the spectrum of one quasi-exactly solvable (QES) periodic potential to that of another QES periodic potential. The self-dual point of this transformation corresponds to the energy-reflection symmetry found previously for certain QES systems. The duality transformation interchanges bands at the bottom (top) of the spectrum of one potential with gaps at the top (bottom) of the spectrum of the other, dual, potential. Thus, the duality transformation provides an exact mapping between the weak coupling (perturbative) and semiclassical (nonperturbative) sectors

Exact self-similar solutions of unsteady ablation flows in inertial confinement fusion; Solutions exactes autosemblables d'ecoulements d'ablation instationnaires en fusion par confinement inertiel

Energy Technology Data Exchange (ETDEWEB)

Boudesocque-Dubois, C.; Gauthier, S.; Clarisse, J.M

2007-07-01

We exhibit and detail the properties of exact self-similar solutions for inviscid compressible ablative flows in slab symmetry with nonlinear heat conduction relevant to inertial confinement fusion (ICF). These solutions have been found after several contributions over the last four decades. We first derived the set of ODEs that governs the self-similar solutions by using the invariance of the Euler's equations with nonlinear heat conduction under the two-parameter Lie group symmetry. A sub-family that leaves the density invariant is detailed since this is the most relevant case for ICF. A physical analysis of these unsteady ablation flows is then provided where the associated dimensionless numbers (Mach, Froude and P let numbers) are calculated. Finally we show that these solutions do not satisfy the constraints of the low Mach number approximation that means that ablation fronts generated within the framework of the present hypotheses (electronic conduction, growing heat flux at the boundary, etc.) cannot be approximated by a steady quasi-incompressible flow as it is often assumed in ICF. Two particular solutions of this family have been recently used for studying stability properties of ablation fronts, since they are representative of the flows that should be reached on the future French Laser MegaJoule. (authors)

Exact soliton-like solutions of perturbed phi4-equation

International Nuclear Information System (INIS)

Gonzalez, J.A.

1986-05-01

Exact soliton-like solutions of damped, driven phi 4 -equation are found. The exact expressions for the velocities of solitons are given. It is non-perturbatively proved that the perturbed phi 4 -equation has stable kink-like solutions of a new type. (author)

Exact solutions of nonlinear differential equations using continued fractions

International Nuclear Information System (INIS)

Ditto, W.L.; Pickett, T.J.

1990-01-01

The continued-fraction conversion method (J. Math. Phys. (N.Y.), 29, 1761 (1988)) is used to generate a homologous family of exact solutions to the Lane-Emden equation φ(r) '' + 2φ(r)'/r + αφ(r) p = 0, for p=5. An exact solution is also obtained for a generalization of the Lane-Emden equation of the form -φ '' (r) -2φ(r)'/r + αφ(r) 2p+1 + λφ(r) 4p+1 = 0 for arbitrary α, γ and p. A condition is established for the generation of exact solutions from the method

Symmetry and exact solutions of nonlinear spinor equations

International Nuclear Information System (INIS)

Fushchich, W.I.; Zhdanov, R.Z.

1989-01-01

This review is devoted to the application of algebraic-theoretical methods to the problem of constructing exact solutions of the many-dimensional nonlinear systems of partial differential equations for spinor, vector and scalar fields widely used in quantum field theory. Large classes of nonlinear spinor equations invariant under the Poincare group P(1, 3), Weyl group (i.e. Poincare group supplemented by a group of scale transformations), and the conformal group C(1, 3) are described. Ansaetze invariant under the Poincare and the Weyl groups are constructed. Using these we reduce the Poincare-invariant nonlinear Dirac equations to systems of ordinary differential equations and construct large families of exact solutions of the nonlinear Dirac-Heisenberg equation depending on arbitrary parameters and functions. In a similar way we have obtained new families of exact solutions of the nonlinear Maxwell-Dirac and Klein-Gordon-Dirac equations. The obtained solutions can be used for quantization of nonlinear equations. (orig.)

New Exact Solutions for (1 + 1)-Dimensional Dispersion-Less System

International Nuclear Information System (INIS)

Naranmandula; Hu Jianguo; Bao Gang; Tubuxin

2008-01-01

Using improved homogeneous balance method, we obtain complex function form new exact solutions for the (1+1)-dimensional dispersion-less system, and from the exact solutions we derive real function form solution of the field u. Based on this real function form solution, we find some new interesting coherent structures by selecting arbitrary functions appropriately

The Quasi-Linear Solution of Vertical Infiltration; La solucion cuasi-lineal de la infiltracion vertical

Energy Technology Data Exchange (ETDEWEB)

Fuentes, Carlos [Instituto Mexicano de Tecnologia del Agua, Jiutepec, Morelos (Mexico); Parlangue, Jean-Yves [Departamento de Agricultura e Ingenieria Biologica (United States); Haverkamp, Randel; Vauclin, Michael [Laboratorio de Estudio de las Transferencias en Hidrologia y Medio ambiente (France)

2001-12-01

The exact solution of the one-dimensional vertical infiltration equation is deducted, when the hydraulic diffusivity is considered constant and the hydraulic conductivity is a combination of both a linear and quadratic functions of the soil water content. This quasi-linear solution includes as particular cases, both the classical solution known as linear soil and the Knight solution. The cumulative infiltrated water as a function of time provided by the quasi-linear solution has been compared with the cumulative infiltrated water obtained from the numerical solution of the Richards equation on three different soils of contrasting hydrodynamic properties. The good agreement between the two solutions has shown that the quasi-linear solution can be used on soils where the accepted hypothesis, on hydraulic diffusivity and hydraulic conductivity, for its deduction is not satisfied. [Spanish] Se deduce la solucion exacta de la ecuacion de la infiltracion unidimensional vertical cuando la difusividad hidraulica es considerada constante y la conductividad hidraulica es una combinacion de una funcion lineal y una cuadratica del contenido volumetrico de agua. Esta solucion cuasi-lineal de la infiltracion contiene, como casos particulares, la solucion clasica conocida como suelo lineal y la solucion de Knight. La lamina infiltrada acumulada en funcion del tiempo proporcionada por la solucion cuasi-lineal se ha comparado con la lamina infiltrada proporcionada por la solucion numerica de la ecuacion de Richards en tres suelos de propiedades hidrodinamicas contrastantes. El buen acuerdo entre las laminas infiltradas ha mostrado que la solucion cuasi-lineal puede utilizarse en suelos donde la difusividad y la conductividad hidraulicas no satisfacen los supuestos de la deduccion.

A class of exact solutions to the Einstein field equations

International Nuclear Information System (INIS)

Goyal, Nisha; Gupta, R K

2012-01-01

The Einstein-Rosen metric is considered and a class of new exact solutions of the field equations for stationary axisymmetric Einstein-Maxwell fields is obtained. The Lie classical approach is applied to obtain exact solutions. 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 Einstein-Maxwell equations. (paper)

Dolan-Grady relations and noncommutative quasi-exactly solvable systems

International Nuclear Information System (INIS)

Klishevich, Sergey M; Plyushchay, Mikhail S

2003-01-01

We investigate a U(1) gauge invariant quantum mechanical system on a 2D noncommutative space with coordinates generating a generalized deformed oscillator algebra. The Hamiltonian is taken as a quadratic form in gauge covariant derivatives obeying the nonlinear Dolan-Grady relations. This restricts the structure function of the deformed oscillator algebra to a quadratic polynomial. The cases when the coordinates form the su(2) and sl(2,R) algebras are investigated in detail. Reducing the Hamiltonian to 1D finite-difference quasi-exactly solvable operators, we demonstrate partial algebraization of the spectrum of the corresponding systems on the fuzzy sphere and noncommutative hyperbolic plane. A completely covariant method based on the notion of intrinsic algebra is proposed to deal with the spectral problem of such systems

On nonlinear differential equation with exact solutions having various pole orders

International Nuclear Information System (INIS)

Kudryashov, N.A.

2015-01-01

We consider a nonlinear ordinary differential equation having solutions with various movable pole order on the complex plane. We show that the pole order of exact solution is determined by values of parameters of the equation. Exact solutions in the form of the solitary waves for the second order nonlinear differential equation are found taking into account the method of the logistic function. Exact solutions of differential equations are discussed and analyzed

New exact travelling wave solutions for the Ostrovsky equation

International Nuclear Information System (INIS)

Kangalgil, Figen; Ayaz, Fatma

2008-01-01

In this Letter, auxiliary equation method is proposed for constructing more general exact solutions of nonlinear partial differential equation with the aid of symbolic computation. In order to illustrate the validity and the advantages of the method we choose the Ostrovsky equation. As a result, many new and more general exact solutions have been obtained for the equation

Exact solutions for some discrete models of the Boltzmann equation

International Nuclear Information System (INIS)

Cabannes, H.; Hong Tiem, D.

1987-01-01

For the simplest of the discrete models of the Boltzmann equation: the Broadwell model, exact solutions have been obtained by Cornille in the form of bisolitons. In the present Note, we build exact solutions for more complex models [fr

Quasi-periodic solutions of nonlinear beam equations with quintic quasi-periodic nonlinearities

Directory of Open Access Journals (Sweden)

Qiuju Tuo

2015-01-01

Full Text Available In this article, we consider the one-dimensional nonlinear beam equations with quasi-periodic quintic nonlinearities $$ u_{tt}+u_{xxxx}+(B+ \\varepsilon\\phi(tu^5=0 $$ under periodic boundary conditions, where B is a positive constant, $\\varepsilon$ is a small positive parameter, $\\phi(t$ is a real analytic quasi-periodic function in t with frequency vector $\\omega=(\\omega_1,\\omega_2,\\dots,\\omega_m$. It is proved that the above equation admits many quasi-periodic solutions by KAM theory and partial Birkhoff normal form.

Dolan Grady relations and noncommutative quasi-exactly solvable systems

Science.gov (United States)

Klishevich, Sergey M.; Plyushchay, Mikhail S.

2003-11-01

We investigate a U(1) gauge invariant quantum mechanical system on a 2D noncommutative space with coordinates generating a generalized deformed oscillator algebra. The Hamiltonian is taken as a quadratic form in gauge covariant derivatives obeying the nonlinear Dolan-Grady relations. This restricts the structure function of the deformed oscillator algebra to a quadratic polynomial. The cases when the coordinates form the {\\mathfrak{su}}(2) and {\\mathfrak{sl}}(2,{\\bb {R}}) algebras are investigated in detail. Reducing the Hamiltonian to 1D finite-difference quasi-exactly solvable operators, we demonstrate partial algebraization of the spectrum of the corresponding systems on the fuzzy sphere and noncommutative hyperbolic plane. A completely covariant method based on the notion of intrinsic algebra is proposed to deal with the spectral problem of such systems.

Exact Solutions of the Harry-Dym Equation

International Nuclear Information System (INIS)

Mokhtari, Reza

2011-01-01

The aim of this paper is to generate exact travelling wave solutions of the Harry-Dym equation through the methods of Adomian decomposition, He's variational iteration, direct integration, and power series. We show that the two later methods are more successful than the two former to obtain more solutions of the equation. (general)

Exact solution of corner-modified banded block-Toeplitz eigensystems

International Nuclear Information System (INIS)

Cobanera, Emilio; Alase, Abhijeet; Viola, Lorenza; Ortiz, Gerardo

2017-01-01

Motivated by the challenge of seeking a rigorous foundation for the bulk-boundary correspondence for free fermions, we introduce an algorithm for determining exactly the spectrum and a generalized-eigenvector basis of a class of banded block quasi-Toeplitz matrices that we call corner-modified . Corner modifications of otherwise arbitrary banded block-Toeplitz matrices capture the effect of boundary conditions and the associated breakdown of translational invariance. Our algorithm leverages the interplay between a non-standard, projector-based method of kernel determination (physically, a bulk-boundary separation) and families of linear representations of the algebra of matrix Laurent polynomials. Thanks to the fact that these representations act on infinite-dimensional carrier spaces in which translation symmetry is restored, it becomes possible to determine the eigensystem of an auxiliary projected block-Laurent matrix. This results in an analytic eigenvector Ansatz , independent of the system size, which we prove is guaranteed to contain the full solution of the original finite-dimensional problem. The actual solution is then obtained by imposing compatibility with a boundary matrix , whose shape is also independent of system size. As an application, we show analytically that eigenvectors of short-ranged fermionic tight-binding models may display power-law corrections to exponential behavior, and demonstrate the phenomenon for the paradigmatic Majorana chain of Kitaev. (paper)

Exact Solutions to a Combined sinh-cosh-Gordon Equation

International Nuclear Information System (INIS)

Wei Long

2010-01-01

Based on a transformed Painleve property and the variable separated ODE method, a function transformation method is proposed to search for exact solutions of some partial differential equations (PDEs) with hyperbolic or exponential functions. This approach provides a more systematical and convenient handling of the solution process of this kind of nonlinear equations. Its key point is to eradicate the hyperbolic or exponential terms by a transformed Painleve property and reduce the given PDEs to a variable-coefficient ordinary differential equations, then we seek for solutions to the resulting equations by some methods. As an application, exact solutions for the combined sinh-cosh-Gordon equation are formally derived. (general)

New explicit and exact solutions of the Benney–Kawahara–Lin equation

International Nuclear Information System (INIS)

Yuan-Xi, Xie

2009-01-01

In this paper, we present a combination method of constructing the explicit and exact solutions of nonlinear partial differential equations. And as an illustrative example, we apply the method to the Benney–Kawahara–Lin equation and derive its many explicit and exact solutions which are all new solutions. (general)

New types of exact solutions for a breaking soliton equation

International Nuclear Information System (INIS)

Mei Jianqin; Zhang Hongqing

2004-01-01

In this paper based on a system of Riccati equations, we present a newly generally projective Riccati equation expansion method and its algorithm, which can be used to construct more new exact solutions of nonlinear differential equations in mathematical physics. A typical breaking soliton equation is chosen to illustrate our algorithm such that more families of new exact solutions are obtained, which contain soliton-like solutions and periodic solutions. This algorithm can also be applied to other nonlinear differential equations

Stochastic epidemic-type model with enhanced connectivity: exact solution

International Nuclear Information System (INIS)

Williams, H T; Mazilu, I; Mazilu, D A

2012-01-01

We present an exact analytical solution to a one-dimensional model of the susceptible–infected–recovered (SIR) epidemic type, with infection rates dependent on nearest-neighbor occupations. We use a quantum mechanical approach, transforming the master equation via a quantum spin operator formulation. We calculate exactly the time-dependent density of infected, recovered and susceptible populations for random initial conditions. Our results compare well with those of previous work, validating the model as a useful tool for additional and extended studies in this important area. Our model also provides exact solutions for the n-point correlation functions, and can be extended to more complex epidemic-type models

Exact solutions and singularities in string theory

International Nuclear Information System (INIS)

Horowitz, G.T.; Tseytlin, A.A.

1994-01-01

We construct two new classes of exact solutions to string theory which are not of the standard plane wave of gauged WZW type. Many of these solutions have curvature singularities. The first class includes the fundamental string solution, for which the string coupling vanishes near the singularity. This suggests that the singularity may not be removed by quantum corrections. The second class consists of hybrids of plane wave and gauged WZW solutions. We discuss a four-dimensional example in detail

Exact solutions to quadratic gravity

Czech Academy of Sciences Publication Activity Database

Pravda, Vojtěch; Pravdová, Alena; Podolský, J.; Švarc, J.

2017-01-01

Roč. 95, č. 8 (2017), č. článku 084025. ISSN 2470-0010 R&D Projects: GA ČR GB14-37086G Institutional support: RVO:67985840 Keywords : quadratic gravity * exact solutions * Kundt spacetimes Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 4.568, year: 2016 https://journals.aps.org/prd/abstract/10.1103/PhysRevD.95.084025

Exact solutions to quadratic gravity

Czech Academy of Sciences Publication Activity Database

Pravda, Vojtěch; Pravdová, Alena; Podolský, J.; Švarc, J.

2017-01-01

Roč. 95, č. 8 (2017), č. článku 084025. ISSN 2470-0010 R&D Projects: GA ČR GB14-37086G Institutional support: RVO:67985840 Keywords : quadratic gravity * exact solutions * Kundt spacetimes Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 4.568, year: 2016 https://journals. aps .org/prd/abstract/10.1103/PhysRevD.95.084025

Exact analytical solutions for nonlinear reaction-diffusion equations

International Nuclear Information System (INIS)

Liu Chunping

2003-01-01

By using a direct method via the computer algebraic system of Mathematica, some exact analytical solutions to a class of nonlinear reaction-diffusion equations are presented in closed form. Subsequently, the hyperbolic function solutions and the triangular function solutions of the coupled nonlinear reaction-diffusion equations are obtained in a unified way

New exact solutions of the Dirac equation

International Nuclear Information System (INIS)

Bagrov, V.G.; Gitman, D.M.; Zadorozhnyj, V.N.; Lavrov, P.M.; Shapovalov, V.N.

1980-01-01

Search for new exact solutions of the Dirac and Klein-Gordon equations are in progress. Considered are general properties of the Dirac equation solutions for an electron in a purely magnetic field, in combination with a longitudinal magnetic and transverse electric fields. New solutions for the equations of charge motion in an electromagnetic field of axial symmetry and in a nonstationary field of a special form have been found for potentials selected concretely

A new auxiliary equation and exact travelling wave solutions of nonlinear equations

International Nuclear Information System (INIS)

Sirendaoreji

2006-01-01

A new auxiliary ordinary differential equation and its solutions are used for constructing exact travelling wave solutions of nonlinear partial differential equations in a unified way. The main idea of this method is to take full advantage of the auxiliary equation which has more new exact solutions. More new exact travelling wave solutions are obtained for the quadratic nonlinear Klein-Gordon equation, the combined KdV and mKdV equation, the sine-Gordon equation and the Whitham-Broer-Kaup equations

Study of coupled nonlinear partial differential equations for finding exact analytical solutions.

Science.gov (United States)

Khan, Kamruzzaman; Akbar, M Ali; Koppelaar, H

2015-07-01

Exact solutions of nonlinear partial differential equations (NPDEs) are obtained via the enhanced (G'/G)-expansion method. The method is subsequently applied to find exact solutions of the Drinfel'd-Sokolov-Wilson (DSW) equation and the (2+1)-dimensional Painlevé integrable Burgers (PIB) equation. The efficiency of this method for finding these exact solutions is demonstrated. The method is effective and applicable for many other NPDEs in mathematical physics.

Exact solutions for the cubic-quintic nonlinear Schroedinger equation

International Nuclear Information System (INIS)

Zhu Jiamin; Ma Zhengyi

2007-01-01

In this paper, the cubic-quintic nonlinear Schroedinger equation is solved through the extended elliptic sub-equation method. As a consequence, many types of exact travelling wave solutions are obtained which including bell and kink profile solitary wave solutions, triangular periodic wave solutions and singular solutions

Finite element approach to solution of multidimensional quasi ...

African Journals Online (AJOL)

problems whose function can be expressed as derivatives and integrated functional or on solution of quasi-harmonic functions whose physical behaviors are governed by a general quasi-harmonic differential equation that can be treated as a quadratic functional that can be minimized over a region. The functional of a ...

Study of coupled nonlinear partial differential equations for finding exact analytical solutions

Science.gov (United States)

Khan, Kamruzzaman; Akbar, M. Ali; Koppelaar, H.

2015-01-01

Exact solutions of nonlinear partial differential equations (NPDEs) are obtained via the enhanced (G′/G)-expansion method. The method is subsequently applied to find exact solutions of the Drinfel'd–Sokolov–Wilson (DSW) equation and the (2+1)-dimensional Painlevé integrable Burgers (PIB) equation. The efficiency of this method for finding these exact solutions is demonstrated. The method is effective and applicable for many other NPDEs in mathematical physics. PMID:26587256

Exact solutions to the Mo-Papas and Landau-Lifshitz equations

Science.gov (United States)

Rivera, R.; Villarroel, D.

2002-10-01

Two exact solutions of the Mo-Papas and Landau-Lifshitz equations for a point charge in classical electrodynamics are presented here. Both equations admit as an exact solution the motion of a charge rotating with constant speed in a circular orbit. These equations also admit as an exact solution the motion of two identical charges rotating with constant speed at the opposite ends of a diameter. These exact solutions allow one to obtain, starting from the equation of motion, a definite formula for the rate of radiation. In both cases the rate of radiation can also be obtained, with independence of the equation of motion, from the well known fields of a point charge, that is, from the Maxwell equations. The rate of radiation obtained from the Mo-Papas equation in the one-charge case coincides with the rate of radiation that comes from the Maxwell equations; but in the two-charge case the results do not coincide. On the other hand, the rate of radiation obtained from the Landau-Lifshitz equation differs from the one that follows from the Maxwell equations in both the one-charge and two-charge cases. This last result does not support a recent statement by Rohrlich in favor of considering the Landau-Lifshitz equation as the correct and exact equation of motion for a point charge in classical electrodynamics.

Exact solutions to the Mo-Papas and Landau-Lifshitz equations

International Nuclear Information System (INIS)

Rivera, R.; Villarroel, D.

2002-01-01

Two exact solutions of the Mo-Papas and Landau-Lifshitz equations for a point charge in classical electrodynamics are presented here. Both equations admit as an exact solution the motion of a charge rotating with constant speed in a circular orbit. These equations also admit as an exact solution the motion of two identical charges rotating with constant speed at the opposite ends of a diameter. These exact solutions allow one to obtain, starting from the equation of motion, a definite formula for the rate of radiation. In both cases the rate of radiation can also be obtained, with independence of the equation of motion, from the well known fields of a point charge, that is, from the Maxwell equations. The rate of radiation obtained from the Mo-Papas equation in the one-charge case coincides with the rate of radiation that comes from the Maxwell equations; but in the two-charge case the results do not coincide. On the other hand, the rate of radiation obtained from the Landau-Lifshitz equation differs from the one that follows from the Maxwell equations in both the one-charge and two-charge cases. This last result does not support a recent statement by Rohrlich in favor of considering the Landau-Lifshitz equation as the correct and exact equation of motion for a point charge in classical electrodynamics

New exact solutions of the Dirac equation. 8

International Nuclear Information System (INIS)

Bagrov, V.G.; Gitman, D.M.; Zadorozhnyj, V.N.; Sukhomlin, N.B.; Shapovalov, V.N.

1978-01-01

The paper continues the investigation into the exact solutions of the Dirac, Klein-Gordon, and Lorentz equations for a charge in an external electromagnetic field. The fields studied do not allow for separation of variables in the Dirac equation, but solutions to the Dirac equation are obtained

New exact solutions of the generalized Zakharov–Kuznetsov ...

Indian Academy of Sciences (India)

In this paper, new exact solutions, including soliton, rational and elliptic integral function solutions, for the generalized Zakharov–Kuznetsov modified equal-width equation are obtained using a new approach called the extended trial equation method. In this discussion, a new version of the trial equation method for the ...

Exact solutions to the Lienard equation and its applications

International Nuclear Information System (INIS)

Feng Zhaosheng

2004-01-01

In this paper, a kind of explicit exact solutions to the Lienard equation is obtained, and the applications of the result in seeking traveling solitary wave solution of the nonlinear Schroedinger equation are presented

A procedure to construct exact solutions of nonlinear evolution ...

Indian Academy of Sciences (India)

Exact solutions; the functional variable method; nonlinear wave equations. PACS Nos 02.30. ... computer science, directly searching for solutions of nonlinear differential equations has become more and ... Right after this pioneer work, this ...

Exact solutions to some modified sine-Gordon equations

International Nuclear Information System (INIS)

Saermark, K.

1983-01-01

Exact, translational solutions to a number of modified sine-Gordon equations are presented. In deriving the equations and the solutions use is made of results from the theory of ordinary differential equations without moving critical points as given by Ince. It is found that kink-like solutions exist also in cases where the coefficients of the trigonometric terms are space- and time-dependent. (Auth.)

Exact interior solutions in 2 + 1-dimensional spacetime

Energy Technology Data Exchange (ETDEWEB)

Rahaman, Farook; Bhar, Piyali [Jadavpur University, Department of Mathematics, Kolkata, West Bengal (India); Biswas, Ritabrata [Indian Institute of Engineering Sceince and Technology Shibpur, Howrah, West Bengal (India); Usmani, A.A. [Aligarh Muslim University, Department of Physics, Aligarh, Uttar Pradesh (India)

2014-04-15

We provide a new class of exact solutions for the interior in 2 + 1-dimensional spacetime. The solutions obtained for the perfect fluid model both with and without cosmological constant (Λ) are found to be regular and singularity free. It assumes very simple analytical forms that help us to study the various physical properties of the configuration. Solutions without Λ are found to be physically acceptable. (orig.)

Exact solitary and periodic wave solutions for a generalized nonlinear Schroedinger equation

International Nuclear Information System (INIS)

Sun Chengfeng; Gao Hongjun

2009-01-01

The generalized nonlinear Schroedinger equation (GNLS) iu t + u xx + β | u | 2 u + γ | u | 4 u + iα (| u | 2 u) x + iτ(| u | 2 ) x u = 0 is studied. Using the bifurcation of travelling waves of this equation, some exact solitary wave solutions were obtained in [Wang W, Sun J,Chen G, Bifurcation, Exact solutions and nonsmooth behavior of solitary waves in the generalized nonlinear Schroedinger equation. Int J Bifucat Chaos 2005:3295-305.]. In this paper, more explicit exact solitary wave solutions and some new smooth periodic wave solutions are obtained.

Exact Solutions for Nonlinear Differential Difference Equations in Mathematical Physics

Directory of Open Access Journals (Sweden)

Khaled A. Gepreel

2013-01-01

Full Text Available We modified the truncated expansion method to construct the exact solutions for some nonlinear differential difference equations in mathematical physics via the general lattice equation, the discrete nonlinear Schrodinger with a saturable nonlinearity, the quintic discrete nonlinear Schrodinger equation, and the relativistic Toda lattice system. Also, we put a rational solitary wave function method to find the rational solitary wave solutions for some nonlinear differential difference equations. The proposed methods are more effective and powerful to obtain the exact solutions for nonlinear difference differential equations.

Exact solutions to some nonlinear PDEs, travelling profiles method

Directory of Open Access Journals (Sweden)

Noureddine Benhamidouche

2008-04-01

\\end{equation*} by a new method that we call the travelling profiles method. This method allows us to find several forms of exact solutions including the classical forms such as travelling-wave and self-similar solutions.

Diffusion kinetics and spinodal decay of quasi-equilibrium solid solutions

International Nuclear Information System (INIS)

Zakharov, M.A.

2000-01-01

Phenomenological theory for rearrangement of solid solutions with the hierarchy of the component atomic mobilities is elaborated in the approximation of the local equilibrium. The hydrodynamic stage of the evolution of these solutions is studied as a sequence of quasi-equilibrium states characterized by implementation of some conditions of the total equilibrium. On the basis of separation of fast and slow constituents of diffusion and on the basis of the method of reduced description one derived equation for evolution of separations of fast components in quasi-equilibrium solid solutions at the arbitrary stages of rearrangement in terms of the generalized lattice model taking account of the proper volumes of the components. The conditions of the stability of quasi-equilibrium solutions to the spinodal decomposition are determined and the equations of metastability boundaries of such systems are derived [ru

A set of exact two soliton wave solutions to Einstein field equations

International Nuclear Information System (INIS)

Wang Youtang; He Zhixian

1991-09-01

A set of exact solutions of Einstein equations in vacuum is obtained. Taking this set of solutions as seed solutions and making use of the Belinsky-Zakharov generation technique a set of generated solutions is constructed. Both set of exact solutions and a set of generated solutions describe two solition waves, which propagate in opposite directions and collide with each other, and then recover their original shapes. The singularities of the two set of solutions are analyzed. The relationship between our solutions and other solutions is also discussed. (author). 11 refs, 4 figs

About simple nonlinear and linear superpositions of special exact solutions of Veselov-Novikov equation

International Nuclear Information System (INIS)

Dubrovsky, V. G.; Topovsky, A. V.

2013-01-01

New exact solutions, nonstationary and stationary, of Veselov-Novikov (VN) equation in the forms of simple nonlinear and linear superpositions of arbitrary number N of exact special solutions u (n) , n= 1, …, N are constructed via Zakharov and Manakov ∂-dressing method. Simple nonlinear superpositions are represented up to a constant by the sums of solutions u (n) and calculated by ∂-dressing on nonzero energy level of the first auxiliary linear problem, i.e., 2D stationary Schrödinger equation. It is remarkable that in the zero energy limit simple nonlinear superpositions convert to linear ones in the form of the sums of special solutions u (n) . It is shown that the sums u=u (k 1 ) +...+u (k m ) , 1 ⩽k 1 2 m ⩽N of arbitrary subsets of these solutions are also exact solutions of VN equation. The presented exact solutions include as superpositions of special line solitons and also superpositions of plane wave type singular periodic solutions. By construction these exact solutions represent also new exact transparent potentials of 2D stationary Schrödinger equation and can serve as model potentials for electrons in planar structures of modern electronics.

The relation among the hyperbolic-function-type exact solutions of nonlinear evolution equations

International Nuclear Information System (INIS)

Liu Chunping; Liu Xiaoping

2004-01-01

First, we investigate the solitary wave solutions of the Burgers equation and the KdV equation, which are obtained by using the hyperbolic function method. Then we present a theorem which will not only give us a clear relation among the hyperbolic-function-type exact solutions of nonlinear evolution equations, but also provide us an approach to construct new exact solutions in complex scalar field. Finally, we apply the theorem to the KdV-Burgers equation and obtain its new exact solutions

Exact Solutions to (2+1)-Dimensional Kaup-Kupershmidt Equation

International Nuclear Information System (INIS)

Lu Hailing; Liu Xiqiang

2009-01-01

In this paper, by using the symmetry method, the relationships between new explicit solutions and old ones of the (2+1)-dimensional Kaup-Kupershmidt (KK) equation are presented. We successfully obtain more general exact travelling wave solutions for (2+1)-dimensional KK equation by the symmetry method and the (G'/G)-expansion method. Consequently, we find some new solutions of (2+1)-dimensional KK equation, including similarity solutions, solitary wave solutions, and periodic solutions. (general)

Quantum decay model with exact explicit analytical solution

Science.gov (United States)

Marchewka, Avi; Granot, Er'El

2009-01-01

A simple decay model is introduced. The model comprises a point potential well, which experiences an abrupt change. Due to the temporal variation, the initial quantum state can either escape from the well or stay localized as a new bound state. The model allows for an exact analytical solution while having the necessary features of a decay process. The results show that the decay is never exponential, as classical dynamics predicts. Moreover, at short times the decay has a fractional power law, which differs from perturbation quantum method predictions. At long times the decay includes oscillations with an envelope that decays algebraically. This is a model where the final state can be either continuous or localized, and that has an exact analytical solution.

Exact solutions for helical magnetohydrodynamic equilibria. II. Nonstatic and nonbarotropic solutions

International Nuclear Information System (INIS)

Villata, M.; Ferrari, A.

1994-01-01

In the framework of the analytical study of magnetohydrodynamic (MHD) equilibria with flow and nonuniform density, a general family of well-behaved exact solutions of the generalized Grad--Shafranov equation and of the whole set of time-independent MHD equations completed by the nonbarotropic ideal gas equation of state is obtained, both in helical and axial symmetry. The helical equilibrium solutions are suggested to be relevant to describe the helical morphology of some astrophysical jets

Exact solutions to nonlinear symmetron theory: One- and two-mirror systems

Science.gov (United States)

Brax, Philippe; Pitschmann, Mario

2018-03-01

We derive the exact analytical solutions to the symmetron field theory equations in the presence of a one- or two-mirror system. The one-dimensional equations of motion are integrated exactly for both systems and their solutions can be expressed in terms of Jacobi elliptic functions. Surprisingly, in the case of two parallel mirrors, the equations of motion generically provide not a unique solution but a discrete set of solutions with increasing number of nodes and energies. The solutions obtained herein can be applied to q BOUNCE experiments, neutron interferometry and for the calculation of the symmetron-field-induced "Casimir force" in the CANNEX experiment.

Exact Solution of a Generalized Nonlinear Schrodinger Equation Dimer

DEFF Research Database (Denmark)

Christiansen, Peter Leth; Maniadis, P.; Tsironis, G.P.

1998-01-01

We present exact solutions for a nonlinear dimer system defined throught a discrete nonlinear Schrodinger equation that contains also an integrable Ablowitz-Ladik term. The solutions are obtained throught a transformation that maps the dimer into a double Sine-Gordon like ordinary nonlinear...... differential equation....

Exact error estimation for solutions of nuclide chain equations

International Nuclear Information System (INIS)

Tachihara, Hidekazu; Sekimoto, Hiroshi

1999-01-01

The exact solution of nuclide chain equations within arbitrary figures is obtained for a linear chain by employing the Bateman method in the multiple-precision arithmetic. The exact error estimation of major calculation methods for a nuclide chain equation is done by using this exact solution as a standard. The Bateman, finite difference, Runge-Kutta and matrix exponential methods are investigated. The present study confirms the following. The original Bateman method has very low accuracy in some cases, because of large-scale cancellations. The revised Bateman method by Siewers reduces the occurrence of cancellations and thereby shows high accuracy. In the time difference method as the finite difference and Runge-Kutta methods, the solutions are mainly affected by the truncation errors in the early decay time, and afterward by the round-off errors. Even though the variable time mesh is employed to suppress the accumulation of round-off errors, it appears to be nonpractical. Judging from these estimations, the matrix exponential method is the best among all the methods except the Bateman method whose calculation process for a linear chain is not identical with that for a general one. (author)

An exact solution in Einstein-Cartan

International Nuclear Information System (INIS)

Roque, W.L.

1982-01-01

The exact solution of the field equations of the Einstein-Cartan theory is obtained for an artificial dust of radially polarized spins, with spherical symmetry and static. For a best estimation of the effect due the spin, the energy-momentum metric tensor is considered null. The gravitational field dynamics is studied for several torsion strengths, through the massive and spinless test-particle moviment, in particular for null torsion Schwarzschild solutions is again obtained. It is observed that the gravitational effects related to the torsin (spin) sometimes are attractives sometimes are repulsives, depending of the torsion values and of the test-particle position and velocity. (L.C.) [pt

Exact solutions of nonlinear generalizations of the Klein Gordon and Schrodinger equations

International Nuclear Information System (INIS)

Burt, P.B.

1978-01-01

Exact solutions of sine Gordon and multiple sine Gordon equations are constructed in terms of solutions of a linear base equation, the Klein Gordon equation and also in terms of nonlinear base equations where the nonlinearity is polynomial in the dependent variable. Further, exact solutions of nonlinear generalizations of the Schrodinger equation and of additional nonlinear generalizations of the Klein Gordon equation are constructed in terms of solutions of linear base equations. Finally, solutions with spherical symmetry, of nonlinear Klein Gordon equations are given. 14 references

Exact compact breather-like solutions of two-dimensional Fermi-Pasta-Ulam lattice

International Nuclear Information System (INIS)

Sarkar, Ranja; Dey, Bishwajyoti

2006-01-01

We demonstrate that two-dimensional Fermi-Pasta-Ulam lattice support exact discrete compact breather-like solutions. We also find exact compact breather solutions of the same lattice in presence of long-range interaction with r -s dependence on the distance in the continuum limit. The usefulness of these solutions for energy localization and transport in various physical systems are discussed. (letter to the editor)

About simple nonlinear and linear superpositions of special exact solutions of Veselov-Novikov equation

Energy Technology Data Exchange (ETDEWEB)

Dubrovsky, V. G.; Topovsky, A. V. [Novosibirsk State Technical University, Karl Marx prosp. 20, Novosibirsk 630092 (Russian Federation)

2013-03-15

New exact solutions, nonstationary and stationary, of Veselov-Novikov (VN) equation in the forms of simple nonlinear and linear superpositions of arbitrary number N of exact special solutions u{sup (n)}, n= 1, Horizontal-Ellipsis , N are constructed via Zakharov and Manakov {partial_derivative}-dressing method. Simple nonlinear superpositions are represented up to a constant by the sums of solutions u{sup (n)} and calculated by {partial_derivative}-dressing on nonzero energy level of the first auxiliary linear problem, i.e., 2D stationary Schroedinger equation. It is remarkable that in the zero energy limit simple nonlinear superpositions convert to linear ones in the form of the sums of special solutions u{sup (n)}. It is shown that the sums u=u{sup (k{sub 1})}+...+u{sup (k{sub m})}, 1 Less-Than-Or-Slanted-Equal-To k{sub 1} < k{sub 2} < Horizontal-Ellipsis < k{sub m} Less-Than-Or-Slanted-Equal-To N of arbitrary subsets of these solutions are also exact solutions of VN equation. The presented exact solutions include as superpositions of special line solitons and also superpositions of plane wave type singular periodic solutions. By construction these exact solutions represent also new exact transparent potentials of 2D stationary Schroedinger equation and can serve as model potentials for electrons in planar structures of modern electronics.

The generalized tanh method to obtain exact solutions of nonlinear partial differential equation

OpenAIRE

Gómez, César

2007-01-01

In this paper, we present the generalized tanh method to obtain exact solutions of nonlinear partial differential equations, and we obtain solitons and exact solutions of some important equations of the mathematical physics.

Exact angular momentum projection based on cranked HFB solution

Energy Technology Data Exchange (ETDEWEB)

Enami, Kenichi; Tanabe, Kosai; Yosinaga, Naotaka [Saitama Univ., Urawa (Japan). Dept. of Physics

1998-03-01

Exact angular momentum projection of cranked HFB solutions is carried out. It is reconfirmed from this calculation that cranked HFB solutions reproduce the intrinsic structure of deformed nucleus. The result also indicates that the energy correction from projection is important for further investigation of nuclear structure. (author)

Fingering patterns in magnetic fluids: Perturbative solutions and the stability of exact stationary shapes

Science.gov (United States)

Anjos, Pedro H. A.; Lira, Sérgio A.; Miranda, José A.

2018-04-01

We examine the formation of interfacial patterns when a magnetic liquid droplet (ferrofluid, or a magnetorheological fluid), surrounded by a nonmagnetic fluid, is subjected to a radial magnetic field in a Hele-Shaw cell. By using a vortex-sheet formalism, we find exact stationary solutions for the fluid-fluid interface in the form of n -fold polygonal shapes. A weakly nonlinear, mode-coupling method is then utilized to find time-evolving perturbative solutions for the interfacial patterns. The stability of such nonzero surface tension exact solutions is checked and discussed, by trying to systematically approach the exact stationary shapes through perturbative solutions containing an increasingly larger number of participating Fourier modes. Our results indicate that the exact stationary solutions of the problem are stable, and that a good matching between exact and perturbative shape solutions is achieved just by using a few Fourier modes. The stability of such solutions is substantiated by a linearization process close to the stationary shape, where a system of mode-coupling equations is diagonalized, determining the eigenvalues which dictate the stability of a fixed point.

Exact and heuristic solutions to the Double TSP with Multiple Stacks

DEFF Research Database (Denmark)

Petersen, Hanne Løhmann; Archetti, Claudia; Madsen, Oli B.G.

-pallet, which can be loaded in 3 stacks in a standard 40 foot container. Different exact and heuristic solution approaches to the DTSPMS have been implemented and tested. The exact approaches are based on different mathematical formulations of the problem which are solved using branch-and-cut. One formulation...... instances. The implemented heuristics include tabu search, simulated annealing and large neighbourhood search. Particularly the LNS approach shows promising results. It finds the known optimal solution of smaller instances (15 orders) within 10 seconds in most cases, and in 3 minutes it finds solutions...

Exact travelling wave solutions for some important nonlinear ...

Indian Academy of Sciences (India)

The study of nonlinear partial differential equations is an active area of research in applied mathematics, theoretical physics and engineering fields. In particular ... In [16–18], the author applied this method to construct the exact solutions of.

New Exact Travelling Wave and Periodic Solutions of Discrete Nonlinear Schroedinger Equation

International Nuclear Information System (INIS)

Yang Qin; Dai Chaoqing; Zhang Jiefang

2005-01-01

Some new exact travelling wave and period solutions of discrete nonlinear Schroedinger equation are found by using a hyperbolic tangent function approach, which was usually presented to find exact travelling wave solutions of certain nonlinear partial differential models. Now we can further extend the new algorithm to other nonlinear differential-different models.

Quasi-integrable non-linear Schrödinger models, infinite towers of exactly conserved charges and bright solitons

Science.gov (United States)

Blas, H.; do Bonfim, A. C. R.; Vilela, A. M.

2017-05-01

Deformations of the focusing non-linear Schrödinger model (NLS) are considered in the context of the quasi-integrability concept. We strengthen the results of JHEP 09 (2012) 103 10.1007/JHEP06(2015)177" TargetType="URL"/> for bright soliton collisions. We addressed the focusing NLS as a complement to the one in JHEP 03 (2016) 005 10.1007/JHEP06(2015)177" TargetType="URL"/> , in which the modified defocusing NLS models with dark solitons were shown to exhibit an infinite tower of exactly conserved charges. We show, by means of analytical and numerical methods, that for certain two-bright-soliton solutions, in which the modulus and phase of the complex modified NLS field exhibit even parities under a space-reflection symmetry, the first four and the sequence of even order charges are exactly conserved during the scattering process of the solitons. We perform extensive numerical simulations and consider the bright solitons with deformed potential V=2η /2+\\upepsilon{({|ψ |}^2)}^{2+\\upepsilon},\\upepsilon \\in \\mathbb{R},η <0 . However, for two-soliton field components without definite parity we also show numerically the vanishing of the first non-trivial anomaly and the exact conservation of the relevant charge. So, the parity symmetry seems to be a sufficient but not a necessary condition for the existence of the infinite tower of conserved charges. The model supports elastic scattering of solitons for a wide range of values of the amplitudes and velocities and the set { η, ɛ}. Since the NLS equation is ubiquitous, our results may find potential applications in several areas of non-linear science.

New exact solutions of sixth-order thin-film equation

Directory of Open Access Journals (Sweden)

Wafaa M. Taha

2014-01-01

Full Text Available TheG′G-expansion method is used for the first time to find traveling-wave solutions for the sixth-order thin-film equation, where related balance numbers are not the usual positive integers. New types of exact traveling-wave solutions, such as – solitary wave solutions, are obtained the sixth-order thin-film equation, when parameters are taken at special values.

New exact solutions of the KdV-Burgers-Kuramoto equation

International Nuclear Information System (INIS)

Zhang Sheng

2006-01-01

A generalized F-expansion method is proposed and applied to the KdV-Burgers-Kuramoto equation. As a result, many new and more general exact travelling wave solutions are obtained including combined non-degenerate Jacobi elliptic function solutions, solitary wave solutions and trigonometric function solutions. The method can be applied to other nonlinear partial differential equations in mathematical physics

Novel correlations in two dimensions: Some exact solutions

International Nuclear Information System (INIS)

Murthy, M.V.; Bhaduri, R.K.; Sen, D.

1996-01-01

We construct a new many-body Hamiltonian with two- and three-body interactions in two space dimensions and obtain its exact many-body ground state for an arbitrary number of particles. This ground state has a novel pairwise correlation. A class of exact solutions for the excited states is also found. These excited states display an energy spectrum similar to the Calogero-Sutherland model in one dimension. The model reduces to an analog of the well-known trigonometric Sutherland model when projected on to a circular ring. copyright 1996 The American Physical Society

The modified simplest equation method to look for exact solutions of nonlinear partial differential equations

OpenAIRE

Efimova, Olga Yu.

2010-01-01

The modification of simplest equation method to look for exact solutions of nonlinear partial differential equations is presented. Using this method we obtain exact solutions of generalized Korteweg-de Vries equation with cubic source and exact solutions of third-order Kudryashov-Sinelshchikov equation describing nonlinear waves in liquids with gas bubbles.

Exact and numerical solutions of generalized Drinfeld-Sokolov equations

International Nuclear Information System (INIS)

Ugurlu, Yavuz; Kaya, Dogan

2008-01-01

In this Letter, we consider a system of generalized Drinfeld-Sokolov (gDS) equations which models one-dimensional nonlinear wave processes in two-component media. We find some exact solutions of gDS by using tanh function method and we also obtain a numerical solution by using the Adomian's Decomposition Method (ADM)

Exact solutions for the (2+1)-dimensional Boiti-Leon-Pempielli system

International Nuclear Information System (INIS)

Hu, Y H; Zheng, C L

2008-01-01

The object reduction approach is applied to the (2+1)-dimensional Boiti-Leon-Pempielli system using a special conditional similarity reduction. Abundant exact solutions of this system, including the hyperboloid function solutions, the trigonometric function solutions and a rational function solution, are obtained

A Table Lookup Method for Exact Analytical Solutions of Nonlinear Fractional Partial Differential Equations

Directory of Open Access Journals (Sweden)

Ji Juan-Juan

2017-01-01

Full Text Available A table lookup method for solving nonlinear fractional partial differential equations (fPDEs is proposed in this paper. Looking up the corresponding tables, we can quickly obtain the exact analytical solutions of fPDEs by using this method. To illustrate the validity of the method, we apply it to construct the exact analytical solutions of four nonlinear fPDEs, namely, the time fractional simplified MCH equation, the space-time fractional combined KdV-mKdV equation, the (2+1-dimensional time fractional Zoomeron equation, and the space-time fractional ZKBBM equation. As a result, many new types of exact analytical solutions are obtained including triangular periodic solution, hyperbolic function solution, singular solution, multiple solitary wave solution, and Jacobi elliptic function solution.

Exact solutions of Lovelock-Born-Infeld black holes

International Nuclear Information System (INIS)

Aiello, Matias; Ferraro, Rafael; Giribet, Gaston

2004-01-01

The exact five-dimensional charged black hole solution in Lovelock gravity coupled to Born-Infeld electrodynamics is presented. This solution interpolates between the Hoffmann black hole for the Einstein-Born-Infeld theory and other solutions in the Lovelock theory previously studied in the literature. It is shown how the conical singularity of the metric around the origin can be removed by a proper choice of the black hole parameters. The differences existing with the Reissner-Nordstroem black holes are discussed. In particular, we show the existence of charged black holes with a unique horizon

Exact Solutions of Five Complex Nonlinear Schrödinger Equations by Semi-Inverse Variational Principle

International Nuclear Information System (INIS)

Najafi Mohammad; Arbabi Somayeh

2014-01-01

In this paper, we establish exact solutions for five complex nonlinear Schrödinger equations. The semi-inverse variational principle (SVP) is used to construct exact soliton solutions of five complex nonlinear Schrödinger equations. Many new families of exact soliton solutions of five complex nonlinear Schrödinger equations are successfully obtained. (general)

Exact and numerical solutions of generalized Drinfeld-Sokolov equations

Energy Technology Data Exchange (ETDEWEB)

Ugurlu, Yavuz [Firat University, Department of Mathematics, 23119 Elazig (Turkey); Kaya, Dogan [Firat University, Department of Mathematics, 23119 Elazig (Turkey)], E-mail: dkaya36@yahoo.com

2008-04-14

In this Letter, we consider a system of generalized Drinfeld-Sokolov (gDS) equations which models one-dimensional nonlinear wave processes in two-component media. We find some exact solutions of gDS by using tanh function method and we also obtain a numerical solution by using the Adomian's Decomposition Method (ADM)

Some exact solutions to the translation-invariant N-body problem

International Nuclear Information System (INIS)

Hall, R.L.

1978-01-01

It is shown that Schroedinger's equation for a translation-invariant system consisting of N particles with arbitrary masses interacting via Hooke's law pair potentials with the same coupling constant can be solved exactly; explicit solutions are found for the case N = 3. Exact solutions are also found explicitly for the translation-invariant problem in which a particle with mass m 0 interacts with N identical particles of mass m 1 via Hooke's law pair potential with coupling constant k 0 2 , and the identical particles interact with each other via Hooke's law pair potentials with coupling constant k 1 2 . The latter solution provides a basis problem for an energy lower-bound method for translation-invariant atom-like systems. (author)

Exact solutions of continuous states for Hartmann potential

International Nuclear Information System (INIS)

Chen Changyuan; Lu Falin; Sun Dongsheng

2004-01-01

In this Letter, we obtain the exact solutions of continuous states for the Hartmann potential. The normalized wave functions of continuous states on the 'k/2π scale' and the calculation formula of phase shifts are presented. Analytical properties of the scattering amplitude are discussed

New exact solutions for two nonlinear equations

International Nuclear Information System (INIS)

Wang Quandi; Tang Minying

2008-01-01

In this Letter, we investigate two nonlinear equations given by u t -u xxt +3u 2 u x =2u x u xx +uu xxx and u t -u xxt +4u 2 u x =3u x u xx +uu xxx . Through some special phase orbits we obtain four new exact solutions for each equation above. Some previous results are extended

Exact solutions of Fisher and Burgers equations with finite transport memory

International Nuclear Information System (INIS)

Kar, Sandip; Banik, Suman Kumar; Ray, Deb Shankar

2003-01-01

The Fisher and Burgers equations with finite memory transport, describing reaction-diffusion and convection-diffusion processes, respectively have recently attracted a lot of attention in the context of chemical kinetics, mathematical biology and turbulence. We show here that they admit exact solutions. While the speed of the travelling wavefront is dependent on the relaxation time in the Fisher equation, memory effects significantly smoothen out the shock wave nature of the Burgers solution, without any influence on the corresponding wave speed. We numerically analyse the ansatz for the exact solution and show that for the reaction-diffusion system the strength of the reaction term must be moderate enough not to exceed a critical limit to allow a travelling wave solution to exist for appreciable finite memory effect

Exact solutions of Fisher and Burgers equations with finite transport memory

CERN Document Server

Kar, S; Ray, D S

2003-01-01

The Fisher and Burgers equations with finite memory transport, describing reaction-diffusion and convection-diffusion processes, respectively have recently attracted a lot of attention in the context of chemical kinetics, mathematical biology and turbulence. We show here that they admit exact solutions. While the speed of the travelling wavefront is dependent on the relaxation time in the Fisher equation, memory effects significantly smoothen out the shock wave nature of the Burgers solution, without any influence on the corresponding wave speed. We numerically analyse the ansatz for the exact solution and show that for the reaction-diffusion system the strength of the reaction term must be moderate enough not to exceed a critical limit to allow a travelling wave solution to exist for appreciable finite memory effect.

New exact travelling wave solutions of bidirectional wave equations

Indian Academy of Sciences (India)

Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Republic of Korea. ∗ ... exact travelling wave solutions of system (1) using the modified tanh–coth function method ... The ordinary differential equation is then integrated.

New exact travelling wave solutions for the generalized nonlinear Schroedinger equation with a source

International Nuclear Information System (INIS)

Abdou, M.A.

2008-01-01

The generalized F-expansion method with a computerized symbolic computation is used for constructing a new exact travelling wave solutions for the generalized nonlinear Schrodinger equation with a source. As a result, many exact travelling wave solutions are obtained which include new periodic wave solution, trigonometric function solutions and rational solutions. The method is straightforward and concise, and it can also be applied to other nonlinear evolution equations in physics

Exact solutions, energy, and charge of stable Q-balls

Energy Technology Data Exchange (ETDEWEB)

Bazeia, D.; Marques, M.A. [Universidade Federal da Paraiba, Departamento de Fisica, Joao Pessoa, PB (Brazil); Menezes, R. [Universidade Federal da Paraiba, Departamento de Ciencias Exatas, Rio Tinto, PB (Brazil); Universidade Federal de Campina Grande, Departamento de Fisica, Campina Grande, PB (Brazil)

2016-05-15

In this work we deal with nontopological solutions of the Q-ball type in two spacetime dimensions. We study models of current interest, described by a Higgs-like and other, similar potentials which unveil the presence of exact solutions. We use the analytic results to investigate how to control the energy and charge to make the Q-balls stable. (orig.)

New quasi-periodic waves of the (2+1)-dimensional sine-Gordon system

International Nuclear Information System (INIS)

Hu, H.C.; Lou, S.Y.

2005-01-01

New exact solutions of the well-known (2+1)-dimensional sine-Gordon system are studied by introducing the modified mapping relations between the cubic nonlinear Klein-Gordon and sine-Gordon equations. Two arbitrary functions are included into the Jacobi elliptic function solutions. By proper selections of the arbitrary functions, new quasi-periodic wave solutions are obtained and displayed graphically

Exact solution for a non-Markovian dissipative quantum dynamics.

Science.gov (United States)

Ferialdi, Luca; Bassi, Angelo

2012-04-27

We provide the exact analytic solution of the stochastic Schrödinger equation describing a harmonic oscillator interacting with a non-Markovian and dissipative environment. This result represents an arrival point in the study of non-Markovian dynamics via stochastic differential equations. It is also one of the few exactly solvable models for infinite-dimensional systems. We compute the Green's function; in the case of a free particle and with an exponentially correlated noise, we discuss the evolution of Gaussian wave functions.

Exact relativistic cylindrical solution of disordered radiation

International Nuclear Information System (INIS)

Fonseca Teixeira, A.F. da; Wolk, I.; Som, M.M.

1976-05-01

A source free disordered distribution of electromagnetic radiation is considered in Einstein' theory, and a time independent exact solution with cylindrical symmetry is obtained. The gravitation and pressure effects of the radiation alone are sufficient to give the distribution an equilibrium. A finite maximum concentration is found on the axis of symmetry, and decreases monotonically to zero outwards. Timelike and null geodesics are discussed

Exact solution of the neutron transport equation in spherical geometry

Energy Technology Data Exchange (ETDEWEB)

Anli, Fikret; Akkurt, Abdullah; Yildirim, Hueseyin; Ates, Kemal [Kahramanmaras Suetcue Imam Univ. (Turkey). Faculty of Sciences and Letters

2017-03-15

Solution of the neutron transport equation in one dimensional slab geometry construct a basis for the solution of neutron transport equation in a curvilinear geometry. Therefore, in this work, we attempt to derive an exact analytical benchmark solution for both neutron transport equations in slab and spherical medium by using P{sub N} approximation which is widely used in neutron transport theory.

Exact solutions of the Wheeler–DeWitt equation and the Yamabe construction

Energy Technology Data Exchange (ETDEWEB)

Ita III, Eyo Eyo, E-mail: ita@usna.edu [Physics Department, US Naval Academy, Annapolis, MD (United States); Soo, Chopin, E-mail: cpsoo@mail.ncku.edu.tw [Department of Physics, National Cheng Kung University, Taiwan (China)

2015-08-15

Exact solutions of the Wheeler–DeWitt equation of the full theory of four dimensional gravity of Lorentzian signature are obtained. They are characterized by Schrödinger wavefunctionals having support on 3-metrics of constant spatial scalar curvature, and thus contain two full physical field degrees of freedom in accordance with the Yamabe construction. These solutions are moreover Gaussians of minimum uncertainty and they are naturally associated with a rigged Hilbert space. In addition, in the limit the regulator is removed, exact 3-dimensional diffeomorphism and local gauge invariance of the solutions are recovered.

New exact travelling wave solutions for two potential coupled KdV equations with symbolic computation

International Nuclear Information System (INIS)

Yang Zonghang

2007-01-01

We find new exact travelling wave solutions for two potential KdV equations which are presented by Foursov [Foursov MV. J Math Phys 2000;41:6173-85]. Compared with the extended tanh-function method, the algorithm used in our paper can obtain some new kinds of exact travelling wave solutions. With the aid of symbolic computation, some novel exact travelling wave solutions of the potential KdV equations are constructed

Further improved F-expansion method and new exact solutions of Konopelchenko-Dubrovsky equation

International Nuclear Information System (INIS)

Wang Dengshan; Zhang Hongqing

2005-01-01

In this paper, with the aid of the symbolic computation we improve the extended F-expansion method in [Chaos, Solitons and Fractals 2004; 22:111] and propose the further improved F-expansion method. Using this method, we have gotten many new exact solutions which we have never seen before within our knowledge of the (2 + 1)-dimensional Konopelchenko-Dubrovsky equation. In addition,the solutions we get are more general than the solutions that the extended F-expansion method gets.The solutions we get include Jacobi elliptic function solutions, soliton-like solutions, trigonometric function solutions and so on. Our method can also apply to other partial differential equations and can also get many new exact solutions

Exact travelling wave solutions for some important nonlinear

Indian Academy of Sciences (India)

The two-dimensional nonlinear physical models and coupled nonlinear systems such as Maccari equations, Higgs equations and Schrödinger–KdV equations have been widely applied in many branches of physics. So, finding exact travelling wave solutions of such equations are very helpful in the theories and numerical ...

The functional variable method for finding exact solutions of some ...

Indian Academy of Sciences (India)

Abstract. In this paper, we implemented the functional variable method and the modified. Riemann–Liouville derivative for the exact solitary wave solutions and periodic wave solutions of the time-fractional Klein–Gordon equation, and the time-fractional Hirota–Satsuma coupled. KdV system. This method is extremely simple ...

Regarding on the exact solutions for the nonlinear fractional differential equations

Directory of Open Access Journals (Sweden)

Kaplan Melike

2016-01-01

Full Text Available In this work, we have considered the modified simple equation (MSE method for obtaining exact solutions of nonlinear fractional-order differential equations. The space-time fractional equal width (EW and the modified equal width (mEW equation are considered for illustrating the effectiveness of the algorithm. It has been observed that all exact solutions obtained in this paper verify the nonlinear ordinary differential equations which was obtained from nonlinear fractional-order differential equations under the terms of wave transformation relationship. The obtained results are shown graphically.

Exact and analytic solutions of the Ernst equation governing axially symmetric stationary vacuum gravitational fields

International Nuclear Information System (INIS)

Baxter, Mathew; Van Gorder, Robert A

2013-01-01

We obtain solutions to a transformation of the axially symmetric Ernst equation, which governs a class of exact solutions of Einstein's field equations. Physically, the equation serves as a model of axially symmetric stationary vacuum gravitational fields. By an application of the method of homotopy analysis, we are able to construct approximate analytic solutions to the relevant boundary value problem in the case where exact solutions are not possible. The results presented constitute a solution for a complicated nonlinear and singular initial value problem. Through appropriate selection of the auxiliary linear operator and convergence control parameter, we are able to obtain low order approximations which minimize residual error over the problem domain. The benefit to such approach is that we obtain very accurate approximations after computing very few terms, hence the computational efficiency is high. Finally, an exact solution is provided in a special case, and this corresponds to the analytical solutions obtained in the more general case. The approximate solutions agree qualitatively with the exact solutions. (paper)

Exact cosmological solutions of Einstein-Maxwell equations as perturbations of the Bertotti-Robinson model

International Nuclear Information System (INIS)

Portugal, R.; Soares, I.D.

1985-01-01

Two new classes of spatially homogeneous cosmological solutions of Einstein-Maxwell equations are obtained by considering a class of exact perturbations of the static Bertotti-Robinson (BR) model. The BR solution is shown to be unstable under these perturbations, being perturbed into exact cosmological solutions with perfect fluid (equations of state p = lambda rho, O [pt

Exact solutions of (3 + 1-dimensional generalized KP equation arising in physics

Directory of Open Access Journals (Sweden)

Syed Tauseef Mohyud-Din

Full Text Available In this work, we have obtained some exact solutions to (3 + 1-dimensional generalized KP Equation. The improved tanϕ(ξ2-expansion method has been introduced to construct the exact solutions of nonlinear evolution equations. The obtained solutions include hyperbolic function solutions, trigonometric function solutions, exponential solutions, and rational solutions. Our study has added some new varieties of solutions to already available solutions. It is also worth mentioning that the computational work has been reduced significantly. Keywords: Improved tanϕ(ξ2-expansion method, Hyperbolic function solution, Trigonometric function solution, Rational solution, (3 + 1-dimensional generalized KP equation

Exact solutions to sine-Gordon-type equations

International Nuclear Information System (INIS)

Liu Shikuo; Fu Zuntao; Liu Shida

2006-01-01

In this Letter, sine-Gordon-type equations, including single sine-Gordon equation, double sine-Gordon equation and triple sine-Gordon equation, are systematically solved by Jacobi elliptic function expansion method. It is shown that different transformations for these three sine-Gordon-type equations play different roles in obtaining exact solutions, some transformations may not work for a specific sine-Gordon equation, while work for other sine-Gordon equations

Stripping reactions in a three-body system. Comparison of DWBA and exact solutions

International Nuclear Information System (INIS)

Brinati, J.R.

1976-01-01

Stripping reactions 'a estados no continuo' are studied in a three particle system. Since the three-body problem has an exact treatment, comparison will be made between the exact solution and the DWBA model solution. This problem is more complex in the continuous case, as shown in the convergence problem of the standard DWBA amplitude radial integral

Exact solutions of generalized Zakharov and Ginzburg-Landau equations

International Nuclear Information System (INIS)

Zhang Jinliang; Wang Mingliang; Gao Kequan

2007-01-01

By using the homogeneous balance principle, the exact solutions of the generalized Zakharov equations and generalized Ginzburg-Landau equation are obtained with the aid of a set of subsidiary higher-order ordinary differential equations (sub-equations for short)

Exact bidirectional X -wave solutions in fiber Bragg gratings

Science.gov (United States)

Efremidis, Nikolaos K.; Nye, Nicholas S.; Christodoulides, Demetrios N.

2017-10-01

We find exact solutions describing bidirectional pulses propagating in fiber Bragg gratings. They are derived by solving the coupled-mode theory equations and are expressed in terms of products of modified Bessel functions with algebraic functions. Depending on the values of the two free parameters, the general bidirectional X -wave solution can also take the form of a unidirectional pulse. We analyze the symmetries and the asymptotic properties of the solutions and also discuss additional waveforms that are obtained by interference of more than one solution. Depending on their parameters, such pulses can create a sharp focus with high contrast.

Asymptotically exact solution of a local copper-oxide model

International Nuclear Information System (INIS)

Zhang Guangming; Yu Lu.

1994-03-01

We present an asymptotically exact solution of a local copper-oxide model abstracted from the multi-band models. The phase diagram is obtained through the renormalization-group analysis of the partition function. In the strong coupling regime, we find an exactly solved line, which crosses the quantum critical point of the mixed valence regime separating two different Fermi-liquid (FL) phases. At this critical point, a many-particle resonance is formed near the chemical potential, and a marginal-FL spectrum can be derived for the spin and charge susceptibilities. (author). 15 refs, 1 fig

Exact self-similar solutions of the Korteweg de Vries equation

International Nuclear Information System (INIS)

Nakach, R.

1975-12-01

It is shown that the exact analytic self-similar solution of the Korteweg de Vries equation is connected with the second Painleve transcendent. When the self-similar independant variable tends to infinity the asymptotic solutions are given by a nonlinear differential equation which can be integrated to yield Jacobian elliptic functions [fr

Exact solutions of Feinberg–Horodecki equation for time-dependent ...

Indian Academy of Sciences (India)

proposed to find the exact solutions of the Feinberg–Horodecki equation for the .... is a polynomial of degree n and satisfies the Rodrigues relation [24] ... The discriminant of expression (15) under the square root has to be zero, so that the.

Exact Travelling Solutions of Discrete sine-Gordon Equation via Extended Tanh-Function Approach

International Nuclear Information System (INIS)

Dai Chaoqing; Zhang Jiefang

2006-01-01

In this paper, we generalize the extended tanh-function approach, which was used to find new exact travelling wave solutions of nonlinear partial differential equations or coupled nonlinear partial differential equations, to nonlinear differential-difference equations. As illustration, two series of exact travelling wave solutions of the discrete sine-Gordon equation are obtained by means of the extended tanh-function approach.

Exact solution of the generalized Peierls equation for arbitrary n-fold screw dislocation

Science.gov (United States)

Wang, Shaofeng; Hu, Xiangsheng

2018-05-01

The exact solution of the generalized Peierls equation is presented and proved for arbitrary n-fold screw dislocation. The displacement field, stress field and the energy of the n-fold dislocation are also evaluated explicitly. It is found that the solution defined on each individual fold is given by the tail cut from the original Peierls solution. In viewpoint of energetics, a screw dislocation has a tendency to spread the distribution on all possible slip planes which are contained in the dislocation line zone. Based on the exact solution, the approximated solution of the improved Peierls equation is proposed for the modified γ-surface.

Exact solutions for oscillators with quadratic damping and mixed-parity nonlinearity

International Nuclear Information System (INIS)

Lai, S K; Chow, K W

2012-01-01

Exact vibration modes of a nonlinear oscillator, which contains both quadratic friction and a mixed-parity restoring force, are derived analytically. Two families of exact solutions are obtained in terms of rational expressions for classical Jacobi elliptic functions. The present solutions allow the investigation of the dynamical behaviour of the system in response to changes in physical parameters that concern nonlinearity. The physical significance of the signs (i.e. attractive or repulsive nature) of the linear, quadratic and cubic restoring forces is discussed. A qualitative analysis is also conducted to provide valuable physical insight into the nature of the system. (paper)

Exact solutions to a schematic nuclear quark model and colorless superconductivity

DEFF Research Database (Denmark)

Bohr, Henrik; da Providencia, Joao

2008-01-01

Exact solutions are found to the equations of a standard nuclear quark model exemplified by the Bonn model which is defined in terms of an effective pairing force. We show, by symmetry arguments, that, in general, the ground state of this model is not color neutral. In particular, color-neutral s......Exact solutions are found to the equations of a standard nuclear quark model exemplified by the Bonn model which is defined in terms of an effective pairing force. We show, by symmetry arguments, that, in general, the ground state of this model is not color neutral. In particular, color...

Exact relativistic solution of disordered radiation with planar symmetry

International Nuclear Information System (INIS)

Teixeira, A.F. Da F.; Wolk, I.; Som, M.M.

1977-01-01

An exact solution of the Einstein equations corresponding to and equilibrium distribution of disordered electromagnetic radiation with planar symmetry is obtained. This equilibrium is due solely to the gravitational and pressure effects inherent to the radiation. The distribution of radiation is found to be maximum and finite at the plane of symmetry, and to decrease monotonically in directions normal to this plane. The solution tends asymptotically to the static plane symmetric vacuum solution obtained by Levi-Civita (Atti. Accad. Naz. Lincei Rc.; 27:240 (1918)). Time-like and null geodesics are discussed. (author)

An Exact Solution of The Neutron Slowing Down Equation

Energy Technology Data Exchange (ETDEWEB)

Stefanovic, D [Boris Kidric Vinca Institute of Nuclear Sciences, Vinca, Belgrade (Yugoslavia)

1970-07-01

The slowing down equation for an infinite homogeneous monoatomic medium is solved exactly. The cross sections depend on neutron energy. The solution is given in analytical form within each of the lethargy intervals. This analytical form is the sum of probabilities which are given by the Green functions. The calculated collision density is compared with the one obtained by Bednarz and also with an approximate Wigner formula for the case of a resonance not wider than one collision interval. For the special case of hydrogen, the present solution reduces to Bethe's solution. (author)

The First-Integral Method and Abundant Explicit Exact Solutions to the Zakharov Equations

Directory of Open Access Journals (Sweden)

Yadong Shang

2012-01-01

Full Text Available This paper is concerned with the system of Zakharov equations which involves the interactions between Langmuir and ion-acoustic waves in plasma. Abundant explicit and exact solutions of the system of Zakharov equations are derived uniformly by using the first integral method. These exact solutions are include that of the solitary wave solutions of bell-type for n and E, the solitary wave solutions of kink-type for E and bell-type for n, the singular traveling wave solutions, periodic wave solutions of triangle functions, Jacobi elliptic function doubly periodic solutions, and Weierstrass elliptic function doubly periodic wave solutions. The results obtained confirm that the first integral method is an efficient technique for analytic treatment of a wide variety of nonlinear systems of partial differential equations.

Dissipative motion perturbation theory and exact solutions

International Nuclear Information System (INIS)

Lodder, J.J.

1976-06-01

Dissipative motion of classical and quantum systems is described. In particular, attention is paid to systems coupled to the radiation field. A dissipative equation of motion for a particle in an arbitrary potential coupled to the radiation field is derived by means of perturbation theory. The usual divrgencies associated with the radiation field are eliminated by the application of a theory of generalized functions. This theory is developed as a subject in its own right and is presented independently. The introduction of classical zero-point energy makes the classical equa tion of motion for the phase density formally the same as its quantum counterpart. In particular, it is shown that the classical zero-point energy prevents the collapse of a classical H-atom and gives rise to a classical ground state. For systems with a quadratic Hamiltoian, the equation of motion can be solved exactly, even in the continuum limit for the radiation field, by means of the new generalized functions. Classically, the Fokker-Planck equation is found without any approximations, and quantum mechanically, the only approximation is the neglect of the change in the ground state caused by the interaction. The derivation is valid even for strong damping and arbitrarily short times. There is no transient time. For harmonic oscillators complete equivalence is shown to exist between quantum mechanics and classical mechanics with zero-point energy. A discussion of the derivation of the Pauli equation is given and perturbation theory is compared with the exact derivation. The exactly solvable models are used to calculate the Langevin force of the radiation field. The result is that the classical Langevin force is exactly delta-correlated, while the quantum Langevin force is not delta-correlated at all. The fluctuation-dissipation theorem is shown to be an exact consequence of the solution to the equations of motion

Exact, multiple soliton solutions of the double sine Gordon equation

International Nuclear Information System (INIS)

Burt, P.B.

1978-01-01

Exact, particular solutions of the double sine Gordon equation in n dimensional space are constructed. Under certain restrictions these solutions are N solitons, where N <= 2q - 1 and q is the dimensionality of space-time. The method of solution, known as the base equation technique, relates solutions of nonlinear partial differential equations to solutions of linear partial differential equations. This method is reviewed and its applicability to the double sine Gordon equation shown explicitly. The N soliton solutions have the remarkable property that they collapse to a single soliton when the wave vectors are parallel. (author)

Exact Solutions for Fractional Differential-Difference Equations by an Extended Riccati Sub-ODE Method

International Nuclear Information System (INIS)

Feng Qinghua

2013-01-01

In this paper, an extended Riccati sub-ODE method is proposed to establish new exact solutions for fractional differential-difference equations in the sense of modified Riemann—Liouville derivative. By a fractional complex transformation, a given fractional differential-difference equation can be turned into another differential-difference equation of integer order. The validity of the method is illustrated by applying it to solve the fractional Hybrid lattice equation and the fractional relativistic Toda lattice system. As a result, some new exact solutions including hyperbolic function solutions, trigonometric function solutions and rational solutions are established. (general)

Exact vacuum solution to conformal Weyl gravity and galactic rotation curves

International Nuclear Information System (INIS)

Mannheim, P.D.; Kazanas, D.

1989-01-01

The complete, exact exterior solution for a static, spherically symmetric source in locally conformal invariant Weyl gravity is presented. The solution includes the familiar exterior Schwarzschild solution as a special case and contains an extra gravitational potential term which grows linearly with distance. The obtained solution provides a potential explanation for observed galactic rotation curves without the need for dark matter. The solution also has some interesting implications for cosmology. 9 refs

Exact solutions of a nonpolynomially nonlinear Schrodinger equation

International Nuclear Information System (INIS)

Parwani, R.; Tan, H.S.

2007-01-01

A nonlinear generalisation of Schrodinger's equation had previously been obtained using information-theoretic arguments. The nonlinearities in that equation were of a nonpolynomial form, equivalent to the occurrence of higher-derivative nonlinear terms at all orders. Here we construct some exact solutions to that equation in 1+1 dimensions. On the half-line, the solutions resemble (exponentially damped) Bloch waves even though no external periodic potential is included. The solutions are nonperturbative as they do not reduce to solutions of the linear theory in the limit that the nonlinearity parameter vanishes. An intriguing feature of the solutions is their infinite degeneracy: for a given energy, there exists a very large arbitrariness in the normalisable wavefunctions. We also consider solutions to a q-deformed version of the nonlinear equation and discuss a natural discretisation implied by the nonpolynomiality. Finally, we contrast the properties of our solutions with other solutions of nonlinear Schrodinger equations in the literature and suggest some possible applications of our results in the domains of low-energy and high-energy physics

Exact solutions and symmetry analysis for the limiting probability distribution of quantum walks

International Nuclear Information System (INIS)

Xu, Xin-Ping; Ide, Yusuke

2016-01-01

In the literature, there are numerous studies of one-dimensional discrete-time quantum walks (DTQWs) using a moving shift operator. However, there is no exact solution for the limiting probability distributions of DTQWs on cycles using a general coin or swapping shift operator. In this paper, we derive exact solutions for the limiting probability distribution of quantum walks using a general coin and swapping shift operator on cycles for the first time. Based on the exact solutions, we show how to generate symmetric quantum walks and determine the condition under which a symmetric quantum walk appears. Our results suggest that choosing various coin and initial state parameters can achieve a symmetric quantum walk. By defining a quantity to measure the variation of symmetry, deviation and mixing time of symmetric quantum walks are also investigated.

Exact solutions and symmetry analysis for the limiting probability distribution of quantum walks

Energy Technology Data Exchange (ETDEWEB)

Xu, Xin-Ping, E-mail: xuxp@mail.ihep.ac.cn [School of Physical Science and Technology, Soochow University, Suzhou 215006 (China); Ide, Yusuke [Department of Information Systems Creation, Faculty of Engineering, Kanagawa University, Yokohama, Kanagawa, 221-8686 (Japan)

2016-10-15

In the literature, there are numerous studies of one-dimensional discrete-time quantum walks (DTQWs) using a moving shift operator. However, there is no exact solution for the limiting probability distributions of DTQWs on cycles using a general coin or swapping shift operator. In this paper, we derive exact solutions for the limiting probability distribution of quantum walks using a general coin and swapping shift operator on cycles for the first time. Based on the exact solutions, we show how to generate symmetric quantum walks and determine the condition under which a symmetric quantum walk appears. Our results suggest that choosing various coin and initial state parameters can achieve a symmetric quantum walk. By defining a quantity to measure the variation of symmetry, deviation and mixing time of symmetric quantum walks are also investigated.

Exact analytic solutions generated from stipulated Morse and trigonometric Scarf potentials

International Nuclear Information System (INIS)

Saikia, N; Ahmed, S A S

2011-01-01

The extended transformation method has been applied to the exactly solvable stipulated Morse potential and trigonometric Scarf potential, to generate a set of exactly solvable quantum systems (QSs) in any chosen dimension. Bound state solutions of the exactly solvable potentials are given. The generated QSs are generally of Sturmian form. We also report a system case-specific regrouping technique to convert a Sturmian QS to a normal QS. A second-order application of the transformation method is given. The normalizability of the generated QSs is generally given in Sturmian form.

The extended hyperbolic function method and exact solutions of the long-short wave resonance equations

International Nuclear Information System (INIS)

Shang Yadong

2008-01-01

The extended hyperbolic functions method for nonlinear wave equations is presented. Based on this method, we obtain a multiple exact explicit solutions for the nonlinear evolution equations which describe the resonance interaction between the long wave and the short wave. The solutions obtained in this paper include (a) the solitary wave solutions of bell-type for S and L, (b) the solitary wave solutions of kink-type for S and bell-type for L, (c) the solitary wave solutions of a compound of the bell-type and the kink-type for S and L, (d) the singular travelling wave solutions, (e) periodic travelling wave solutions of triangle function types, and solitary wave solutions of rational function types. The variety of structure to the exact solutions of the long-short wave equation is illustrated. The methods presented here can also be used to obtain exact solutions of nonlinear wave equations in n dimensions

Normal stress differences from Oldroyd 8-constant framework: Exact analytical solution for large-amplitude oscillatory shear flow

Science.gov (United States)

Saengow, C.; Giacomin, A. J.

2017-12-01

The Oldroyd 8-constant framework for continuum constitutive theory contains a rich diversity of popular special cases for polymeric liquids. In this paper, we use part of our exact solution for shear stress to arrive at unique exact analytical solutions for the normal stress difference responses to large-amplitude oscillatory shear (LAOS) flow. The nonlinearity of the polymeric liquids, triggered by LAOS, causes these responses at even multiples of the test frequency. We call responses at a frequency higher than twice the test frequency higher harmonics. We find the new exact analytical solutions to be compact and intrinsically beautiful. These solutions reduce to those of our previous work on the special case of the corotational Maxwell fluid. Our solutions also agree with our new truncated Goddard integral expansion for the special case of the corotational Jeffreys fluid. The limiting behaviors of these exact solutions also yield new explicit expressions. Finally, we use our exact solutions to see how η∞ affects the normal stress differences in LAOS.

Symbolic computation of exact solutions for a nonlinear evolution equation

International Nuclear Information System (INIS)

Liu Yinping; Li Zhibin; Wang Kuncheng

2007-01-01

In this paper, by means of the Jacobi elliptic function method, exact double periodic wave solutions and solitary wave solutions of a nonlinear evolution equation are presented. It can be shown that not only the obtained solitary wave solutions have the property of loop-shaped, cusp-shaped and hump-shaped for different values of parameters, but also different types of double periodic wave solutions are possible, namely periodic loop-shaped wave solutions, periodic hump-shaped wave solutions or periodic cusp-shaped wave solutions. Furthermore, periodic loop-shaped wave solutions will be degenerated to loop-shaped solitary wave solutions for the same values of parameters. So do cusp-shaped solutions and hump-shaped solutions. All these solutions are new and first reported here

Nonlinear differential equations with exact solutions expressed via the Weierstrass function

NARCIS (Netherlands)

Kudryashov, NA

2004-01-01

A new problem is studied, that is to find nonlinear differential equations with special solutions expressed via the Weierstrass function. A method is discussed to construct nonlinear ordinary differential equations with exact solutions. The main step of our method is the assumption that nonlinear

EXACT SOLITARY WAVE SOLUTIONS TO A CLASS OF NONLINEAR DIFFERENTIAL EQUATIONS USING DIRECT ALGEBRAIC METHOD

Institute of Scientific and Technical Information of China (English)

无

2008-01-01

Using direct algebraic method,exact solitary wave solutions are performed for a class of third order nonlinear dispersive disipative partial differential equations. These solutions are obtained under certain conditions for the relationship between the coefficients of the equation. The exact solitary waves of this class are rational functions of real exponentials of kink-type solutions.

Logical gaps in the approximate solutions of the social learning game and an exact solution.

Science.gov (United States)

Dai, Wenjie; Wang, Xin; Di, Zengru; Wu, Jinshan

2014-01-01

After the social learning models were proposed, finding solutions to the games becomes a well-defined mathematical question. However, almost all papers on the games and their applications are based on solutions built either upon an ad-hoc argument or a twisted Bayesian analysis of the games. Here, we present logical gaps in those solutions and offer an exact solution of our own. We also introduce a minor extension to the original game so that not only logical differences but also differences in action outcomes among those solutions become visible.

New exact solutions of coupled Boussinesq–Burgers equations by Exp-function method

Directory of Open Access Journals (Sweden)

L.K. Ravi

2017-03-01

Full Text Available In the present paper, we build the new analytical exact solutions of a nonlinear differential equation, specifically, coupled Boussinesq–Burgers equations by means of Exp-function method. Then, we analyze the results by plotting the three dimensional soliton graphs for each case, which exhibit the simplicity and effectiveness of the proposed method. The primary purpose of this paper is to employ a new approach, which allows us victorious and efficient derivation of the new analytical exact solutions for the coupled Boussinesq–Burgers equations.

Exact traveling wave solutions of fractional order Boussinesq-like equations by applying Exp-function method

Directory of Open Access Journals (Sweden)

Rahmatullah

2018-03-01

Full Text Available We have computed new exact traveling wave solutions, including complex solutions of fractional order Boussinesq-Like equations, occurring in physical sciences and engineering, by applying Exp-function method. The method is blended with fractional complex transformation and modified Riemann-Liouville fractional order operator. Our obtained solutions are verified by substituting back into their corresponding equations. To the best of our knowledge, no other technique has been reported to cope with the said fractional order nonlinear problems combined with variety of exact solutions. Graphically, fractional order solution curves are shown to be strongly related to each other and most importantly, tend to fixate on their integer order solution curve. Our solutions comprise high frequencies and very small amplitude of the wave responses. Keywords: Exp-function method, New exact traveling wave solutions, Modified Riemann-Liouville derivative, Fractional complex transformation, Fractional order Boussinesq-like equations, Symbolic computation

ExactPack Documentation

Energy Technology Data Exchange (ETDEWEB)

Singleton, Robert Jr. [Los Alamos National Laboratory; Israel, Daniel M. [Los Alamos National Laboratory; Doebling, Scott William [Los Alamos National Laboratory; Woods, Charles Nathan [Los Alamos National Laboratory; Kaul, Ann [Los Alamos National Laboratory; Walter, John William Jr [Los Alamos National Laboratory; Rogers, Michael Lloyd [Los Alamos National Laboratory

2016-05-09

For code verification, one compares the code output against known exact solutions. There are many standard test problems used in this capacity, such as the Noh and Sedov problems. ExactPack is a utility that integrates many of these exact solution codes into a common API (application program interface), and can be used as a stand-alone code or as a python package. ExactPack consists of python driver scripts that access a library of exact solutions written in Fortran or Python. The spatial profiles of the relevant physical quantities, such as the density, fluid velocity, sound speed, or internal energy, are returned at a time specified by the user. The solution profiles can be viewed and examined by a command line interface or a graphical user interface, and a number of analysis tools and unit tests are also provided. We have documented the physics of each problem in the solution library, and provided complete documentation on how to extend the library to include additional exact solutions. ExactPack’s code architecture makes it easy to extend the solution-code library to include additional exact solutions in a robust, reliable, and maintainable manner.

Exact asymptotic expansions for solutions of multi-dimensional renewal equations

International Nuclear Information System (INIS)

Sgibnev, M S

2006-01-01

We derive expansions with exact asymptotic expressions for the remainders for solutions of multi-dimensional renewal equations. The effect of the roots of the characteristic equation on the asymptotic representation of solutions is taken into account. The resulting formulae are used to investigate the asymptotic behaviour of the average number of particles in age-dependent branching processes having several types of particles

Some exact solutions for maximally symmetric topological defects in Anti de Sitter space

Science.gov (United States)

Alvarez, Orlando; Haddad, Matthew

2018-03-01

We obtain exact analytical solutions for a class of SO( l) Higgs field theories in a non-dynamic background n-dimensional anti de Sitter space. These finite transverse energy solutions are maximally symmetric p-dimensional topological defects where n = ( p + 1) + l. The radius of curvature of anti de Sitter space provides an extra length scale that allows us to study the equations of motion in a limit where the masses of the Higgs field and the massive vector bosons are both vanishing. We call this the double BPS limit. In anti de Sitter space, the equations of motion depend on both p and l. The exact analytical solutions are expressed in terms of standard special functions. The known exact analytical solutions are for kink-like defects ( p = 0 , 1 , 2 , . . . ; l = 1), vortex-like defects ( p = 1 , 2 , 3; l = 2), and the 't Hooft-Polyakov monopole ( p = 0; l = 3). A bonus is that the double BPS limit automatically gives a maximally symmetric classical glueball type solution. In certain cases where we did not find an analytic solution, we present numerical solutions to the equations of motion. The asymptotically exponentially increasing volume with distance of anti de Sitter space imposes different constraints than those found in the study of defects in Minkowski space.

Exact solutions for scalar field cosmology in f(R) gravity

Science.gov (United States)

Maharaj, S. D.; Goswami, R.; Chervon, S. V.; Nikolaev, A. V.

2017-09-01

We study scalar field FLRW cosmology in the content of f(R) gravity. Our consideration is restricted to the spatially flat Friedmann universe. We derived the general evolution equations of the model, and showed that the scalar field equation is automatically satisfied for any form of the f(R) function. We also derived representations for kinetic and potential energies, as well as for the acceleration in terms of the Hubble parameter and the form of the f(R) function. Next we found the exact cosmological solutions in modified gravity without specifying the f(R) function. With negligible acceleration of the scalar curvature, we found that the de Sitter inflationary solution is always attained. Also we obtained new solutions with special restrictions on the integration constants. These solutions contain oscillating, accelerating, decelerating and even contracting universes. For further investigation, we selected special cases which can be applied with early or late inflation. We also found exact solutions for the general case for the model with negligible acceleration of the scalar curvature in terms of special Airy functions. Using initial conditions which represent the universe at the present epoch, we determined the constants of integration. This allows for the comparison of the scale factor in the new solutions with that for current stage of the universe evolution in the ΛCDM model.

Exact closed-form solutions of a fully nonlinear asymptotic two-fluid model

Science.gov (United States)

Cheviakov, Alexei F.

2018-05-01

A fully nonlinear model of Choi and Camassa (1999) describing one-dimensional incompressible dynamics of two non-mixing fluids in a horizontal channel, under a shallow water approximation, is considered. An equivalence transformation is presented, leading to a special dimensionless form of the system, involving a single dimensionless constant physical parameter, as opposed to five parameters present in the original model. A first-order dimensionless ordinary differential equation describing traveling wave solutions is analyzed. Several multi-parameter families of physically meaningful exact closed-form solutions of the two-fluid model are derived, corresponding to periodic, solitary, and kink-type bidirectional traveling waves; specific examples are given, and properties of the exact solutions are analyzed.

Exact solutions to two higher order nonlinear Schroedinger equations

International Nuclear Information System (INIS)

Xu Liping; Zhang Jinliang

2007-01-01

Using the homogeneous balance principle and F-expansion method, the exact solutions to two higher order nonlinear Schroedinger equations which describe the propagation of femtosecond pulses in nonlinear fibres are obtained with the aid of a set of subsidiary higher order ordinary differential equations (sub-equations for short)

Exact solutions of the neutron slowing down equation

International Nuclear Information System (INIS)

Dawn, T.Y.; Yang, C.N.

1976-01-01

The problem of finding the exact analytic closed-form solution for the neutron slowing down equation in an infinite homogeneous medium is studied in some detail. The existence and unique properties of the solution of this equation for both the time-dependent and the time-independent cases are studied. A direct method is used to determine the solution of the stationary problem. The final result is given in terms of a sum of indefinite multiple integrals by which solutions of some special cases and the Placzek-type oscillation are examined. The same method can be applied to the time-dependent problem with the aid of the Laplace transformation technique, but the inverse transform is, in general, laborious. However, the solutions of two special cases are obtained explicitly. Results are compared with previously reported works in a variety of cases. The time moments for the positive integral n are evaluated, and the conditions for the existence of the negative moments are discussed

Exact solution of the N-dimensional generalized Dirac-Coulomb equation

International Nuclear Information System (INIS)

Tutik, R.S.

1992-01-01

An exact solution to the bound state problem for the N-dimensional generalized Dirac-Coulomb equation, whose potential contains both the Lorentz-vector and Lorentz-scalar terms of the Coulomb form, is obtained. 24 refs. (author)

Exact scattering solutions in an energy sudden (ES) representation

International Nuclear Information System (INIS)

Chang, B.; Eno, L.; Rabitz, H.

1983-01-01

In this paper, we lay down the theoretical foundations for computing exact scattering wave functions in a reference frame which moves in unison with the system internal coordinates. In this frame the (internal) coordinates appear to be fixed and its adoption leads very naturally (in zeroth order) to the energy sudden (ES) approximation [and the related infinite order sudden (IOS) method]. For this reason we call the new representation for describing the exact dynamics of a many channel scattering problem, the ES representation. Exact scattering solutions are derived in both time dependent and time independent frameworks for the representation and many interesting results in these frames are established. It is shown, e.g., that in a time dependent frame the usual Schroedinger propagator factorizes into internal Hamiltonian, ES, and energy correcting propagators. We also show that in a time independent frame the full Green's functions can be similarly factorized. Another important feature of the new representation is that it forms a firm foundation for seeking corrections to the ES approximation. Thus, for example, the singularity which arises in conventional perturbative expansions of the full Green's functions (with the ES Green's function as the zeroth order solution) is avoided in the ES representation. Finally, a number of both time independent and time dependent ES correction schemes are suggested

Exact soliton-like solutions of the radial Gross–Pitaevskii equation

International Nuclear Information System (INIS)

Toikka, L A; Hietarinta, J; Suominen, K-A

2012-01-01

We construct exact ring soliton-like solutions of the cylindrically symmetric (i.e. radial) Gross–Pitaevskii equation with a potential, using the similarity transformation method. Depending on the choice of the allowed free functions, the solutions can take the form of stationary dark or bright rings whose time dependence is in the phase dynamics only, or oscillating and bouncing solutions, related to the second Painlevé transcendent. In each case the potential can be chosen to be time independent. (paper)

Exact solutions to operator differential equations

International Nuclear Information System (INIS)

Bender, C.M.

1992-01-01

In this talk we consider the Heisenberg equations of motion q = -i(q, H), p = -i(p, H), for the quantum-mechanical Hamiltonian H(p, q) having one degree of freedom. It is a commonly held belief that such operator differential equations are intractable. However, a technique is presented here that allows one to obtain exact, closed-form solutions for huge classes of Hamiltonians. This technique, which is a generalization of the classical action-angle variable methods, allows us to solve, albeit formally and implicitly, the operator differential equations of two anharmonic oscillators whose Hamiltonians are H = p 2 /2 + q 4 /4 and H = p 4 /4 + q 4 /4

Exact solutions to a nonlinear dispersive model with variable coefficients

International Nuclear Information System (INIS)

Yin Jun; Lai Shaoyong; Qing Yin

2009-01-01

A mathematical technique based on an auxiliary differential equation and the symbolic computation system Maple is employed to investigate a prototypical and nonlinear K(n, n) equation with variable coefficients. The exact solutions to the equation are constructed analytically under various circumstances. It is shown that the variable coefficients and the exponent appearing in the equation determine the quantitative change in the physical structures of the solutions.

New family of exact solutions for colliding plane gravitational waves

International Nuclear Information System (INIS)

Yurtsever, U.

1988-01-01

We construct an infinite-parameter family of exact solutions to the vacuum Einstein field equations describing colliding gravitational plane waves with parallel polarizations. The interaction regions of the solutions in this family are locally isometric to the interiors of those static axisymmetric (Weyl) black-hole solutions which admit both a nonsingular horizon, and an analytic extension of the exterior metric to the interior of the horizon. As a member of this family of solutions we also obtain, for the first time, a colliding plane-wave solution where both of the two incoming plane waves are purely anastigmatic, i.e., where both incoming waves have equal focal lengths

Exact solutions for an oscillator with anti-symmetric quadratic nonlinearity

Science.gov (United States)

Beléndez, A.; Martínez, F. J.; Beléndez, T.; Pascual, C.; Alvarez, M. L.; Gimeno, E.; Arribas, E.

2018-04-01

Closed-form exact solutions for an oscillator with anti-symmetric quadratic nonlinearity are derived from the first integral of the nonlinear differential equation governing the behaviour of this oscillator. The mathematical model is an ordinary second order differential equation in which the sign of the quadratic nonlinear term changes. Two parameters characterize this oscillator: the coefficient of the linear term and the coefficient of the quadratic term. Not only the common case in which both coefficients are positive but also all possible combinations of positive and negative signs of these coefficients which provide periodic motions are considered, giving rise to four different cases. Three different periods and solutions are obtained, since the same result is valid in two of these cases. An interesting feature is that oscillatory motions whose equilibrium points are not at x = 0 are also considered. The periods are given in terms of an incomplete or complete elliptic integral of the first kind, and the exact solutions are expressed as functions including Jacobi elliptic cosine or sine functions.

An Algebraic Method for Constructing Exact Solutions to Difference-Differential Equations

International Nuclear Information System (INIS)

Wang Zhen; Zhang Hongqing

2006-01-01

In this paper, we present a method to solve difference differential equation(s). As an example, we apply this method to discrete KdV equation and Ablowitz-Ladik lattice equation. As a result, many exact solutions are obtained with the help of Maple including soliton solutions presented by hyperbolic functions sinh and cosh, periodic solutions presented by sin and cos and rational solutions. This method can also be used to other nonlinear difference-differential equation(s).

5D Lovelock gravity: New exact solutions with torsion

Science.gov (United States)

Cvetković, B.; Simić, D.

2016-10-01

Five-dimensional Lovelock gravity is investigated in the first order formalism. A new class of exact solutions is constructed: the Bañados, Teitelboim, Zanelli black rings with and without torsion. We show that our solution with torsion exists in a different sector of the Lovelock gravity, as compared to the Lovelock Chern-Simons sector or the one investigated by Canfora et al. The conserved charges of the solutions are found using Nester's formula, and the results are confirmed by the canonical method. We show that the theory linearized around the background with torsion possesses two additional degrees of freedom with respect to general relativity.

Class of nonsingular exact solutions for Laplacian pattern formation

International Nuclear Information System (INIS)

Mineev-Weinstein, M.B.; Dawson, S.P.

1994-01-01

We present a class of exact solutions for the so-called Laplacian growth equation describing the zero-surface-tension limit of a variety of two-dimensional pattern formation problems. These solutions are free of finite-time singularities (cusps) for quite general initial conditions. They reproduce various features of viscous fingering observed in experiments and numerical simulations with surface tension, such as existence of stagnation points, screening, tip splitting, and coarsening. In certain cases the asymptotic interface consists of N separated moving Saffman-Taylor fingers

An Exact Solution of the Gamma Ray Burst Arrival Time Analysis ...

Indian Academy of Sciences (India)

R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22

An Exact Solution of the Gamma Ray Burst Arrival Time Analysis. Problem. S. Sinha ISRO Satellite Center, Bangalore 560 017, India. Abstract. An analytical solution of the GRB arrival time analysis is presented. The errors in the position of the GRB resulting from timing and position errors of different satellites are calculated.

Water hammer (with FSI): exact solution : parallelization and application

NARCIS (Netherlands)

Loh, K.; Tijsseling, A.S.

2014-01-01

The 1D fully coupled Fluid-Structure Interaction (FSI) model can adequately describe the water hammer effect on the fluid, and the structural behaviour of the pipe. This paper attempts to increase the capability of using an exact solution of the 1D FSI problem applied to a straight pipe with a

New exact solutions of Einstein's field equations: gravitational force can also be repulsive!

International Nuclear Information System (INIS)

Dietz, W.

1988-01-01

This article has not been written for specialists of exact solutions of Einstein's field equations but for physicists who are interested in nontrivial information on this topic. We recall the history and some basic properties of exact solutions of Einstein's vacuum equations. We show that the field equations for stationary axisymmetric vacuum gravitational fields can be expressed by only one nonlinear differential equation for a complex function. This compact form of the field equations allows the generation of almost all stationary axisymmetric vacuum gravitational fields. We present a new stationary two-body solution of Einstein's equations as an application of this generation technique. This new solution proves the existence of a macroscopic, repulsive spin-spin interaction in general relativity. Some estimates that are related to this new two-body solution are given

Exact solutions of Einstein and Einstein-scalar equations in 2+1 dimensions

International Nuclear Information System (INIS)

Virbhadra, K.S.

1995-01-01

A nonstatic and circularly symmetric exact solution of the Einstein equations (with a cosmological constant Λ and null fluid) in 2 + 1 dimensions is given. This is a nonstatic generalization of the uncharged spinless Bandos Teitelboim Zanelli (BTZ) metric. For Λ = 0, spacetime is though not flat, the Kretschmann invariant vanishes. The energy, momentum, and power output for this metric are obtained. Further a static and circularly symmetric exact solution of the Einstein-massless scalar equations is given, which has a curvature singularity at r=0 and the scalar field diverges at r=0 as well as at infinity. (author). 12 refs

Exact solutions to the time-fractional differential equations via local fractional derivatives

Science.gov (United States)

Guner, Ozkan; Bekir, Ahmet

2018-01-01

This article utilizes the local fractional derivative and the exp-function method to construct the exact solutions of nonlinear time-fractional differential equations (FDEs). For illustrating the validity of the method, it is applied to the time-fractional Camassa-Holm equation and the time-fractional-generalized fifth-order KdV equation. Moreover, the exact solutions are obtained for the equations which are formed by different parameter values related to the time-fractional-generalized fifth-order KdV equation. This method is an reliable and efficient mathematical tool for solving FDEs and it can be applied to other non-linear FDEs.

Exact Solutions of the Time Fractional BBM-Burger Equation by Novel (G′/G-Expansion Method

Directory of Open Access Journals (Sweden)

Muhammad Shakeel

2014-01-01

Full Text Available The fractional derivatives are used in the sense modified Riemann-Liouville to obtain exact solutions for BBM-Burger equation of fractional order. This equation can be converted into an ordinary differential equation by using a persistent fractional complex transform and, as a result, hyperbolic function solutions, trigonometric function solutions, and rational solutions are attained. The performance of the method is reliable, useful, and gives newer general exact solutions with more free parameters than the existing methods. Numerical results coupled with the graphical representation completely reveal the trustworthiness of the method.

A self-tuning exact solution and the non-existence of horizons in 5d gravity-scalar system

International Nuclear Information System (INIS)

Zhu Chuan-Jie; Abdus Salam International Centre for Theoretical Physics, Trieste

2000-05-01

We present an exact thick domain wall solution with naked singularities to five dimensional gravity coupled with a scalar field with exponential potential. In our solution we found exactly the special coefficient of the exponent as coming from compactification of string theory with cosmological constant. We show that this solution is self-tuning when a 3-brane is included. In searching for a solution with horizon we found a similar exact solution with fine-tuned exponent coefficient with an integration constant. Failing to find a solution with horizon we prove the non-existence of horizons. These naked singularities actually can't be resolved by horizon. We also comment on the physical relevance of this solution. (author)

Exact solution of nonrelativistic Schrodinger equation for certain central physical potential

International Nuclear Information System (INIS)

Bose, S.K.; Gupta, N.

1998-01-01

It is obtained here a class/classes of exact solution of the nonrelativistic Schrodinger equation for certain central potentials of physical interest by using proper ansatz/ansatze. The explicit expressions of energy eigenvalue and eigenfunction are obtained for each solution. These solutions are valid when for, in general, each solutions an interrelation between the parameters of the potential and the orbital-angular-momentum quantum number l is satisfied. These solutions, besides having an aesthetic appeal, can be used as benchmark to test the accuracy of nonperturbative methods, which sometimes yield wrong results, of solving the Schrodinger equation. The exact solution for the following central potentials, which are relevant in different areas of physics, have been obtained: 1) V(r)=ar 6 + br 4 + cr 2 ; 2) V(r)=ar 2 + br + c/r; 3) V(r)=r 2 + λr 2 /(1+gr 2 ); 4) V(r)= a/r + b/(r+λ); 5a) V(r)=a/r + b/r 2 +c/r 3 +d/r 4 ; 5)b V(r)=a/r 2 + b/r 2 + c/r 4 + d/r 6 ; 6a) V(r)=a/r 1/2 + b/r 3/2 ; 6b) V(r)=ar 2/3 + br -2/3 + cr -4/3

A new sub-equation method applied to obtain exact travelling wave solutions of some complex nonlinear equations

International Nuclear Information System (INIS)

Zhang Huiqun

2009-01-01

By using a new coupled Riccati equations, a direct algebraic method, which was applied to obtain exact travelling wave solutions of some complex nonlinear equations, is improved. And the exact travelling wave solutions of the complex KdV equation, Boussinesq equation and Klein-Gordon equation are investigated using the improved method. The method presented in this paper can also be applied to construct exact travelling wave solutions for other nonlinear complex equations.

An Exact Solution to the Central Core Model of the Renal Medulla

Science.gov (United States)

Mickens, Ronald E.

1998-11-01

The central core model of the renal medulla provides a mathematical representation of the urine concentration mechanism. The model consists of eight coupled, nonlinear ODE's subject to certain initial and boundary conditions. Many investigators have studied the properties of the solutions to these equations, however no general analytic solution is known to exist. Thus, special exact solutions assume a position of significance by providing a basis for insight into the understanding of more realistic models used to analyze actual data. We calculate an exact solution for the case in which the water permeabilities are zero and a particular, but realistic, functional form is used for the metabolic pump. A detailed discussion will be given for the results obtained on the four cencentration and four flux functions that define the model. If invited to do so, the author is willing to expand the talk for the above abstract to twenty minutes.

Exact bright and dark spatial soliton solutions in saturable nonlinear media

International Nuclear Information System (INIS)

Calvo, Gabriel F.; Belmonte-Beitia, Juan; Perez-Garcia, Victor M.

2009-01-01

We present exact analytical bright and dark (black and grey) solitary wave solutions of a nonlinear Schroedinger-type equation describing the propagation of spatial beams in media exhibiting a saturable nonlinearity (such as centrosymmetric photorefractive materials). A qualitative study of the stationary equation is carried out together with a discussion of the stability of the solutions.

Exact solutions for a discrete unidimensional Boltzmann model satisfying all conservation laws

International Nuclear Information System (INIS)

Cornille, H.

1989-01-01

We consider a four-velocity discrete and unidimensional Boltzmann model. The mass, momentum and energy conservation laws being satisfied we can define a temperature. We report the exact positive solutions which have been found: periodic in the space and propagating or not when the time is growing, shock waves similarity solutions and (1 + 1)-dimensional solutions [fr

Wireless three-hop networks with stealing II : exact solutions through boundary value problems

NARCIS (Netherlands)

Guillemin, F.; Knessl, C.; Leeuwaarden, van J.S.H.

2013-01-01

We study the stationary distribution of a random walk in the quarter plane arising in the study of three-hop wireless networks with stealing. Our motivation is to find exact tail asymptotics (beyond logarithmic estimates) for the marginal distributions, which requires an exact solution for the

New analytical exact solutions of time fractional KdV-KZK equation by Kudryashov methods

Science.gov (United States)

S Saha, Ray

2016-04-01

In this paper, new exact solutions of the time fractional KdV-Khokhlov-Zabolotskaya-Kuznetsov (KdV-KZK) equation are obtained by the classical Kudryashov method and modified Kudryashov method respectively. For this purpose, the modified Riemann-Liouville derivative is used to convert the nonlinear time fractional KdV-KZK equation into the nonlinear ordinary differential equation. In the present analysis, the classical Kudryashov method and modified Kudryashov method are both used successively to compute the analytical solutions of the time fractional KdV-KZK equation. As a result, new exact solutions involving the symmetrical Fibonacci function, hyperbolic function and exponential function are obtained for the first time. The methods under consideration are reliable and efficient, and can be used as an alternative to establish new exact solutions of different types of fractional differential equations arising from mathematical physics. The obtained results are exhibited graphically in order to demonstrate the efficiencies and applicabilities of these proposed methods of solving the nonlinear time fractional KdV-KZK equation.

Exact solutions of fractional mBBM equation and coupled system of fractional Boussinesq-Burgers

Science.gov (United States)

Javeed, Shumaila; Saif, Summaya; Waheed, Asif; Baleanu, Dumitru

2018-06-01

The new exact solutions of nonlinear fractional partial differential equations (FPDEs) are established by adopting first integral method (FIM). The Riemann-Liouville (R-L) derivative and the local conformable derivative definitions are used to deal with the fractional order derivatives. The proposed method is applied to get exact solutions for space-time fractional modified Benjamin-Bona-Mahony (mBBM) equation and coupled time-fractional Boussinesq-Burgers equation. The suggested technique is easily applicable and effectual which can be implemented successfully to obtain the solutions for different types of nonlinear FPDEs.

Exact solution to the Coulomb wave using the linearized phase-amplitude method

Directory of Open Access Journals (Sweden)

Shuji Kiyokawa

2015-08-01

Full Text Available The author shows that the amplitude equation from the phase-amplitude method of calculating continuum wave functions can be linearized into a 3rd-order differential equation. Using this linearized equation, in the case of the Coulomb potential, the author also shows that the amplitude function has an analytically exact solution represented by means of an irregular confluent hypergeometric function. Furthermore, it is shown that the exact solution for the Coulomb potential reproduces the wave function for free space expressed by the spherical Bessel function. The amplitude equation for the large component of the Dirac spinor is also shown to be the linearized 3rd-order differential equation.

General method and exact solutions to a generalized variable-coefficient two-dimensional KdV equation

International Nuclear Information System (INIS)

Chen, Yong; Shanghai Jiao-Tong Univ., Shangai; Chinese Academy of sciences, Beijing

2005-01-01

A general method to uniformly construct exact solutions in terms of special function of nonlinear partial differential equations is presented by means of a more general ansatz and symbolic computation. Making use of the general method, we can successfully obtain the solutions found by the method proposed by Fan (J. Phys. A., 36 (2003) 7009) and find other new and more general solutions, which include polynomial solutions, exponential solutions, rational solutions, triangular periodic wave solution, soliton solutions, soliton-like solutions and Jacobi, Weierstrass doubly periodic wave solutions. A general variable-coefficient two-dimensional KdV equation is chosen to illustrate the method. As a result, some new exact soliton-like solutions are obtained. planets. The numerical results are given in tables. The results are discussed in the conclusion

Painlevé test for integrability and exact solutions for the field ...

Indian Academy of Sciences (India)

- tion between two pairs of solutions. ... have been rediscovered. Keywords. Painlevé analysis; integrability; auto-Backlund transformations; exact solu- ..... [8] H Yoshida, Celestial Mechanics 81, 363 (1983). [9] H Yoshida, Celestial Mechanics ...

Exact solution for four-order acousto-optic Bragg diffraction with arbitrary initial conditions.

Science.gov (United States)

Pieper, Ron; Koslover, Deborah; Poon, Ting-Chung

2009-03-01

An exact solution to the four-order acousto-optic (AO) Bragg diffraction problem with arbitrary initial conditions compatible with exact Bragg angle incident light is developed. The solution, obtained by solving a 4th-order differential equation, is formalized into a transition matrix operator predicting diffracted light orders at the exit of the AO cell in terms of the same diffracted light orders at the entrance. It is shown that the transition matrix is unitary and that this unitary matrix condition is sufficient to guarantee energy conservation. A comparison of analytical solutions with numerical predictions validates the formalism. Although not directly related to the approach used to obtain the solution, it was discovered that all four generated eigenvalues from the four-order AO differential matrix operator are expressed simply in terms of Euclid's Divine Proportion.

The exact solutions and approximate analytic solutions of the (2 + 1)-dimensional KP equation based on symmetry method.

Science.gov (United States)

Gai, Litao; Bilige, Sudao; Jie, Yingmo

2016-01-01

In this paper, we successfully obtained the exact solutions and the approximate analytic solutions of the (2 + 1)-dimensional KP equation based on the Lie symmetry, the extended tanh method and the homotopy perturbation method. In first part, we obtained the symmetries of the (2 + 1)-dimensional KP equation based on the Wu-differential characteristic set algorithm and reduced it. In the second part, we constructed the abundant exact travelling wave solutions by using the extended tanh method. These solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions respectively. It should be noted that when the parameters are taken as special values, some solitary wave solutions are derived from the hyperbolic function solutions. Finally, we apply the homotopy perturbation method to obtain the approximate analytic solutions based on four kinds of initial conditions.

Exact Solutions of Atmospheric (2+1)-Dimensional Nonlinear Incompressible Non-hydrostatic Boussinesq Equations

Science.gov (United States)

Liu, Ping; Wang, Ya-Xiong; Ren, Bo; Li, Jin-Hua

2016-12-01

Exact solutions of the atmospheric (2+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq (INHB) equations are researched by Combining function expansion and symmetry method. By function expansion, several expansion coefficient equations are derived. Symmetries and similarity solutions are researched in order to obtain exact solutions of the INHB equations. Three types of symmetry reduction equations and similarity solutions for the expansion coefficient equations are proposed. Non-traveling wave solutions for the INHB equations are obtained by symmetries of the expansion coefficient equations. Making traveling wave transformations on expansion coefficient equations, we demonstrate some traveling wave solutions of the INHB equations. The evolutions on the wind velocities, temperature perturbation and pressure perturbation are demonstrated by figures, which demonstrate the periodic evolutions with time and space. Supported by the National Natural Science Foundation of China under Grant Nos. 11305031 and 11305106, and Training Programme Foundation for Outstanding Young Teachers in Higher Education Institutions of Guangdong Province under Grant No. Yq2013205

New Exact Solutions for the Wick-Type Stochastic Kudryashov–Sinelshchikov Equation

International Nuclear Information System (INIS)

Ray, S. Saha; Singh, S.

2017-01-01

In this article, exact solutions of Wick-type stochastic Kudryashov–Sinelshchikov equation have been obtained by using improved Sub-equation method. We have used Hermite transform for transforming the Wick-type stochastic Kudryashov–Sinelshchikov equation to deterministic partial differential equation. Also we have applied inverse Hermite transform for obtaining a set of stochastic solutions in the white noise space. (paper)

Discrete Symmetries Analysis and Exact Solutions of the Inviscid Burgers Equation

Directory of Open Access Journals (Sweden)

Hongwei Yang

2012-01-01

Full Text Available We discuss the Lie point symmetries and discrete symmetries of the inviscid Burgers equation. By employing the Lie group method of infinitesimal transformations, symmetry reductions and similarity solutions of the governing equation are given. Based on discrete symmetries analysis, two groups of discrete symmetries are obtained, which lead to new exact solutions of the inviscid Burgers equation.

Elastic stars in general relativity: III. Stiff ultrarigid exact solutions

International Nuclear Information System (INIS)

Karlovini, Max; Samuelsson, Lars

2004-01-01

We present an equation of state for elastic matter which allows for purely longitudinal elastic waves in all propagation directions, not just principal directions. The speed of these waves is equal to the speed of light whereas the transversal type speeds are also very high, comparable to but always strictly less than that of light. Clearly such an equation of state does not give a reasonable matter description for the crust of a neutron star, but it does provide a nice causal toy model for an extremely rigid phase in a neutron star core, should such a phase exist. Another reason for focusing on this particular equation of state is simply that it leads to a very simple recipe for finding stationary rigid motion exact solutions to the Einstein equations. In fact, we show that a very large class of stationary spacetimes with constant Ricci scalar can be interpreted as rigid motion solutions with this matter source. We use the recipe to derive a static spherically symmetric exact solution with constant energy density, regular centre and finite radius, having a nontrivial parameter that can be varied to yield a mass-radius curve from which stability can be read off. It turns out that the solution is stable down to a tenuity R/M slightly less than 3. The result of this static approach to stability is confirmed by a numerical determination of the fundamental radial oscillation mode frequency. We also present another solution with outwards decreasing energy density. Unfortunately, this solution only has a trivial scaling parameter and is found to be unstable

Exact solutions of the vacuum Einstein's equations allowing for two noncommuting Killing vectors

International Nuclear Information System (INIS)

Aliev, V.N.; Leznov, A.N.

1990-01-01

Einstein's equations are written in the form of covariant gauge theory in two-dimensional space with binomial solvable gauge group, with respect to two noncommutative of Killing vectors. The theory is exact integrable in one-dimensional case and series of partial exact solutions are constructed in two-dimensional. 5 refs

Some exact solutions to the Lighthill–Whitham–Richards–Payne traffic flow equations

International Nuclear Information System (INIS)

Rowlands, G; Infeld, E; Skorupski, A A

2013-01-01

We find a class of exact solutions to the Lighthill–Whitham–Richards–Payne (LWRP) traffic flow equations. Using two consecutive Lagrangian transformations, a linearization is achieved. Next, depending on the initial density, we either apply (again two) Lambert functions and obtain exact formulae for the dependence of the car density and velocity on x, t, or else, failing that, the same result in a parametric representation. The calculation always involves two possible factorizations of a consistency condition. Both must be considered. In physical terms, the lineup usually separates into two offshoots at different velocities. Each velocity soon becomes uniform. This outcome in many ways resembles the two soliton solution to the Korteweg–de Vries equation. We check general conservation requirements. Although traffic flow research has developed tremendously since LWRP, this calculation, being exact, may open the door to solving similar problems, such as gas dynamics or water flow in rivers. With this possibility in mind, we outline the procedure in some detail at the end. (paper)

Convergence acceleration of quasi-periodic and quasi-periodic-rational interpolations by polynomial corrections

OpenAIRE

Lusine Poghosyan

2014-01-01

The paper considers convergence acceleration of the quasi-periodic and the quasi-periodic-rational interpolations by application of polynomial corrections. We investigate convergence of the resultant quasi-periodic-polynomial and quasi-periodic-rational-polynomial interpolations and derive exact constants of the main terms of asymptotic errors in the regions away from the endpoints. Results of numerical experiments clarify behavior of the corresponding interpolations for moderate number of in...

Exact solutions of time-dependent Dirac equations and the quantum-classical correspondence

International Nuclear Information System (INIS)

Zhang Zhiguo

2006-01-01

Exact solutions to the Dirac equations with a time-dependent mass and a static magnetic field or a time-dependent linear potential are given. Matrix elements of the coordinate, momentum and velocity operator are calculated. In the large quantum number limit, these matrix elements give the classical solution

Exact Closed-form Solutions for Lamb's Problem

Science.gov (United States)

Feng, X.

2017-12-01

In this work, we report on an exact closedform solution for the displacement at the surfaceof an elastic halfspace elicited by a buried point source that acts at some point underneath thatsurface. This is commonly referred to as the 3D Lamb's problem, for which previous solutionswere restricted to sources and receivers placed at the free surface. By means of the reciprocitytheorem, our solution should also be valid as a means to obtain the displacements at interior pointswhen the source is placed at the free surface. We manage to obtain explicit results by expressingthe solution in terms of elementary algebraic expression as well as elliptic integrals. We anchorour developments on Poissons ratio 0.25 starting from Johnson's numerical, integral transformsolutions. Furthermore, the spatial derivatives of our solutions can be easily acquired in termsof our methods. In the end, our closed-form results agree perfectly with the numerical results ofJohnson, which strongly conrms the correctness of our explicit formulas. It is hoped that in duetime, these formulas may constitute a valuable canonical solution that will serve as a yardstickagainst which other numerical solutions can be compared and measured.In addition, we abstract some terms from our solutions as the generator of the Rayleigh waves.Some basic properties of the Rayleigh waves in the time domain will be indicated in terms of thegenerator. The fareld radiation patterns of P-wave and S-wave elicited by the double-couple forcein the uniform half-space medium could also be acquired from our results.

The exact fundamental solution for the Benes tracking problem

Science.gov (United States)

Balaji, Bhashyam

2009-05-01

The universal continuous-discrete tracking problem requires the solution of a Fokker-Planck-Kolmogorov forward equation (FPKfe) for an arbitrary initial condition. Using results from quantum mechanics, the exact fundamental solution for the FPKfe is derived for the state model of arbitrary dimension with Benes drift that requires only the computation of elementary transcendental functions and standard linear algebra techniques- no ordinary or partial differential equations need to be solved. The measurement process may be an arbitrary, discrete-time nonlinear stochastic process, and the time step size can be arbitrary. Numerical examples are included, demonstrating its utility in practical implementation.

New approach to the exact solution of viscous flow due to stretching (shrinking and porous sheet

Directory of Open Access Journals (Sweden)

Azhar Ali

Full Text Available Exact analytical solutions for the generalized stretching (shrinking of a porous surface, for the variable suction (injection velocity, is presented in this paper. The solution is generalized in the sense that the existing solutions that correspond to various stretching velocities are recovered as a special case of this study. A suitable similarity transformation is introduced to find self-similar solution of the non-linear governing equations. The flow is characterized by a few non-dimensional parameters signifying the problem completely. These parameters are such that the whole range of stretching (shrinking problems discussed earlier can be recovered by assigning appropriate values to these parameters. A key point of the whole narrative is that a number of earlier works can be abridged into one generalized problem through the introduction of a new similarity transformation and finding its exact solution encompassing all the earlier solutions. Keywords: Exact solutions, New similarities, Permeable and moving sheet

Exact solutions to chaotic and stochastic systems

Science.gov (United States)

González, J. A.; Reyes, L. I.; Guerrero, L. E.

2001-03-01

We investigate functions that are exact solutions to chaotic dynamical systems. A generalization of these functions can produce truly random numbers. For the first time, we present solutions to random maps. This allows us to check, analytically, some recent results about the complexity of random dynamical systems. We confirm the result that a negative Lyapunov exponent does not imply predictability in random systems. We test the effectiveness of forecasting methods in distinguishing between chaotic and random time series. Using the explicit random functions, we can give explicit analytical formulas for the output signal in some systems with stochastic resonance. We study the influence of chaos on the stochastic resonance. We show, theoretically, the existence of a new type of solitonic stochastic resonance, where the shape of the kink is crucial. Using our models we can predict specific patterns in the output signal of stochastic resonance systems.

Exact Riemann solutions of the Ripa model for flat and non-flat bottom topographies

Science.gov (United States)

Rehman, Asad; Ali, Ishtiaq; Qamar, Shamsul

2018-03-01

This article is concerned with the derivation of exact Riemann solutions for Ripa model considering flat and non-flat bottom topographies. The Ripa model is a system of shallow water equations accounting for horizontal temperature gradients. In the case of non-flat bottom topography, the mass, momentum and energy conservation principles are utilized to relate the left and right states across the step-type bottom topography. The resulting system of algebraic equations is solved iteratively. Different numerical case studies of physical interest are considered. The solutions obtained from developed exact Riemann solvers are compared with the approximate solutions of central upwind scheme.

Exact solutions for a system of nonlinear plasma fluid equations

International Nuclear Information System (INIS)

Prahovic, M.G.; Hazeltine, R.D.; Morrison, P.J.

1991-04-01

A method is presented for constructing exact solutions to a system of nonlinear plasma fluid equations that combines the physics of reduced magnetohydrodynamics and the electrostatic drift-wave description of the Charney-Hasegawa-Mima equation. The system has nonlinearities that take the form of Poisson brackets involving the fluid field variables. The method relies on modifying a class of simple equilibrium solutions, but no approximations are made. A distinguishing feature is that the original nonlinear problem is reduced to the solution of two linear partial differential equations, one fourth-order and the other first-order. The first-order equation has Hamiltonian characteristics and is easily integrated, supplying information about the general structure of solutions. 6 refs

Exact traveling wave solutions of fractional order Boussinesq-like equations by applying Exp-function method

Science.gov (United States)

Rahmatullah; Ellahi, Rahmat; Mohyud-Din, Syed Tauseef; Khan, Umar

2018-03-01

We have computed new exact traveling wave solutions, including complex solutions of fractional order Boussinesq-Like equations, occurring in physical sciences and engineering, by applying Exp-function method. The method is blended with fractional complex transformation and modified Riemann-Liouville fractional order operator. Our obtained solutions are verified by substituting back into their corresponding equations. To the best of our knowledge, no other technique has been reported to cope with the said fractional order nonlinear problems combined with variety of exact solutions. Graphically, fractional order solution curves are shown to be strongly related to each other and most importantly, tend to fixate on their integer order solution curve. Our solutions comprise high frequencies and very small amplitude of the wave responses.

Explicit and exact solutions for a generalized long-short wave resonance equations with strong nonlinear term

International Nuclear Information System (INIS)

Shang Yadong

2005-01-01

In this paper, the evolution equations with strong nonlinear term describing the resonance interaction between the long wave and the short wave are studied. Firstly, based on the qualitative theory and bifurcation theory of planar dynamical systems, all of the explicit and exact solutions of solitary waves are obtained by qualitative seeking the homoclinic and heteroclinic orbits for a class of Lienard equations. Then the singular travelling wave solutions, periodic travelling wave solutions of triangle functions type are also obtained on the basis of the relationships between the hyperbolic functions and that between the hyperbolic functions with the triangle functions. The varieties of structure of exact solutions of the generalized long-short wave equation with strong nonlinear term are illustrated. The methods presented here also suitable for obtaining exact solutions of nonlinear wave equations in multidimensions

Exact Solution of the Six-Vertex Model with Domain Wall Boundary Conditions. Disordered Phase

CERN Document Server

Bleher, P M

2005-01-01

The six-vertex model, or the square ice model, with domain wall boundary conditions (DWBC) has been introduced and solved for finite $N$ by Korepin and Izergin. The solution is based on the Yang-Baxter equations and it represents the free energy in terms of an $N\\times N$ Hankel determinant. Paul Zinn-Justin observed that the Izergin-Korepin formula can be re-expressed in terms of the partition function of a random matrix model with a nonpolynomial interaction. We use this observation to obtain the large $N$ asymptotics of the six-vertex model with DWBC in the disordered phase. The solution is based on the Riemann-Hilbert approach and the Deift-Zhou nonlinear steepest descent method. As was noticed by Kuperberg, the problem of enumeration of alternating sign matrices (the ASM problem) is a special case of the the six-vertex model. We compare the obtained exact solution of the six-vertex model with known exact results for the 1, 2, and 3 enumerations of ASMs, and also with the exact solution on the so-called f...

New analytical exact solutions of time fractional KdV–KZK equation by Kudryashov methods

International Nuclear Information System (INIS)

Saha Ray, S

2016-01-01

In this paper, new exact solutions of the time fractional KdV–Khokhlov–Zabolotskaya–Kuznetsov (KdV–KZK) equation are obtained by the classical Kudryashov method and modified Kudryashov method respectively. For this purpose, the modified Riemann–Liouville derivative is used to convert the nonlinear time fractional KdV–KZK equation into the nonlinear ordinary differential equation. In the present analysis, the classical Kudryashov method and modified Kudryashov method are both used successively to compute the analytical solutions of the time fractional KdV–KZK equation. As a result, new exact solutions involving the symmetrical Fibonacci function, hyperbolic function and exponential function are obtained for the first time. The methods under consideration are reliable and efficient, and can be used as an alternative to establish new exact solutions of different types of fractional differential equations arising from mathematical physics. The obtained results are exhibited graphically in order to demonstrate the efficiencies and applicabilities of these proposed methods of solving the nonlinear time fractional KdV–KZK equation. (paper)

Exact solutions for the higher-order nonlinear Schoerdinger equation in nonlinear optical fibres

International Nuclear Information System (INIS)

Liu Chunping

2005-01-01

First, by using the generally projective Riccati equation method, many kinds of exact solutions for the higher-order nonlinear Schoerdinger equation in nonlinear optical fibres are obtained in a unified way. Then, some relations among these solutions are revealed

Covariant two-particle wave functions for model quasipotential allowing exact solutions

International Nuclear Information System (INIS)

Kapshaj, V.N.; Skachkov, N.B.

1982-01-01

Two formulations of quasipotential equations in the relativistic configurational representation are considered for the wave function of relative motion of a bound state of two relativistic particles. Exact solutions of these equations are found for some model quasipotentials

Hot 56Mn reactions in permanganate solutions: a quasi solution state study [Paper No. NC-6

International Nuclear Information System (INIS)

Dedgaonkar, V.G.; Mitra, S.

1982-01-01

Neutron activation of aqueous solutions of transition metal and ammonium permanganates over the concentration range 1-10 -3 M has been performed. Retentions for concentrated solutions were much higher than the solid state values, and upon dilution, a limiting value of approx. 4 per cent was attained. Activation of 1-10 -1 M permanganate quasi solutions containing either alumina or a polystyrene cation exchanger allowed continuous extraction of the recoil species before their recombination. (author)

Discrete coupled derivative nonlinear Schroedinger equations and their quasi-periodic solutions

International Nuclear Information System (INIS)

Geng Xianguo; Su Ting

2007-01-01

A hierarchy of nonlinear differential-difference equations associated with a discrete isospectral problem is proposed, in which a typical differential-difference equation is a discrete coupled derivative nonlinear Schroedinger equation. With the help of the nonlinearization of the Lax pairs, the hierarchy of nonlinear differential-difference equations is decomposed into a new integrable symplectic map and a class of finite-dimensional integrable Hamiltonian systems. Based on the theory of algebraic curve, the Abel-Jacobi coordinates are introduced to straighten out the corresponding flows, from which quasi-periodic solutions for these differential-difference equations are obtained resorting to the Riemann-theta functions. Moreover, a (2+1)-dimensional discrete coupled derivative nonlinear Schroedinger equation is proposed and its quasi-periodic solutions are derived

New exact solution for the exterior gravitational field of a spinning mass

International Nuclear Information System (INIS)

Manko, V.S.

1990-01-01

An exact asymptotically flat solution of the vacuum Einstein equations representing the exterior gravitational field of a stationary axisymmetric mass with an arbitrary mass-multipole structure is presented

Covariant two-particle wave functions for model quasipotentials admitting exact solutions

International Nuclear Information System (INIS)

Kapshaj, V.N.; Skachkov, N.B.

1983-01-01

Two formulations of quasipotential equations in the relativistic configurational representation are considered for the wave function of the internal motion of the bound system of two relativistic particles. Exact solutions of these equations are found for some model quasipotentials

Nonlinear reaction-diffusion equations with delay: some theorems, test problems, exact and numerical solutions

Science.gov (United States)

Polyanin, A. D.; Sorokin, V. G.

2017-12-01

The paper deals with nonlinear reaction-diffusion equations with one or several delays. We formulate theorems that allow constructing exact solutions for some classes of these equations, which depend on several arbitrary functions. Examples of application of these theorems for obtaining new exact solutions in elementary functions are provided. We state basic principles of construction, selection, and use of test problems for nonlinear partial differential equations with delay. Some test problems which can be suitable for estimating accuracy of approximate analytical and numerical methods of solving reaction-diffusion equations with delay are presented. Some examples of numerical solutions of nonlinear test problems with delay are considered.

Exact solutions of the Navier-Stokes equations generalized for flow in porous media

Science.gov (United States)

Daly, Edoardo; Basser, Hossein; Rudman, Murray

2018-05-01

Flow of Newtonian fluids in porous media is often modelled using a generalized version of the full non-linear Navier-Stokes equations that include additional terms describing the resistance to flow due to the porous matrix. Because this formulation is becoming increasingly popular in numerical models, exact solutions are required as a benchmark of numerical codes. The contribution of this study is to provide a number of non-trivial exact solutions of the generalized form of the Navier-Stokes equations for parallel flow in porous media. Steady-state solutions are derived in the case of flows in a medium with constant permeability along the main direction of flow and a constant cross-stream velocity in the case of both linear and non-linear drag. Solutions are also presented for cases in which the permeability changes in the direction normal to the main flow. An unsteady solution for a flow with velocity driven by a time-periodic pressure gradient is also derived. These solutions form a basis for validating computational models across a wide range of Reynolds and Darcy numbers.

Exact solution of a quantum forced time-dependent harmonic oscillator

Science.gov (United States)

Yeon, Kyu Hwang; George, Thomas F.; Um, Chung IN

1992-01-01

The Schrodinger equation is used to exactly evaluate the propagator, wave function, energy expectation values, uncertainty values, and coherent state for a harmonic oscillator with a time dependent frequency and an external driving time dependent force. These quantities represent the solution of the classical equation of motion for the time dependent harmonic oscillator.

Bifurcations of Exact Traveling Wave Solutions for (2+1)-Dimensional HNLS Equation

International Nuclear Information System (INIS)

Xu Yuanfen

2012-01-01

For the (2+1)-Dimensional HNLS equation, what are the dynamical behavior of its traveling wave solutions and how do they depend on the parameters of the systems? This paper will answer these questions by using the methods of dynamical systems. Ten exact explicit parametric representations of the traveling wave solutions are given. (general)

Exact explicit travelling wave solutions for (n + 1)-dimensional Klein-Gordon-Zakharov equations

International Nuclear Information System (INIS)

Li Jibin

2007-01-01

Using the methods of dynamical systems for the (n + 1)-dimensional KGS nonlinear wave equations, five classes of exact explicit parametric representations of the bounded travelling solutions are obtained. To guarantee the existence of the above solutions, all parameter conditions are given

Exact traveling wave solutions for a new nonlinear heat transfer equation

Directory of Open Access Journals (Sweden)

Gao Feng

2017-01-01

Full Text Available In this paper, we propose a new non-linear partial differential equation to de-scribe the heat transfer problems at the extreme excess temperatures. Its exact traveling wave solutions are obtained by using Cornejo-Perez and Rosu method.

Exact solution of planar and nonplanar weak shock wave problem in gasdynamics

International Nuclear Information System (INIS)

Singh, L.P.; Ram, S.D.; Singh, D.B.

2011-01-01

Highlights: → An exact solution is derived for a problem of weak shock wave in adiabatic gas dynamics. → The density ahead of the shock is taken as a power of the position from the origin of the shock wave. → For a planar and non-planar motion, the total energy carried by the wave varies with respect to time. → The solution obtained for the planer, and cylindrically symmetric flow is new one. → The results obtained are also presented graphically for different Mach numbers. - Abstract: In the present paper, an analytical approach is used to determine a new exact solution of the problem of one dimensional unsteady adiabatic flow of planer and non-planer weak shock waves in an inviscid ideal fluid. Here it is assumed that the density ahead of the shock front varies according to the power law of the distance from the source of disturbance. The solution of the problem is presented in the form of a power in the distance and the time.

Exact interior solutions for static spheres in the Einstein-Cartan theory with two sources of torsion

CERN Document Server

Gallakhmetov, A M

2002-01-01

In the framework of the problem of existence of exact interior solutions for static spherically symmetric configurations in the Einstein-Cartan theory (ECT), the distributions of perfect fluid and non-minimally coupled scalar field are considered. The exact solutions in the one-torsion ECT and two-torsion one are obtained. Some consequences of two sources of torsion are discussed.

The potts chain in a random field: an exact solution

International Nuclear Information System (INIS)

Riera, R.; Chaves, C.M.G.F.; Santos, Raimundo R. dos.

1984-01-01

An exact solution is presented for the one-dimensional q-state Potts model in a quenched random field. The ferromagnetic phase is unstable against any small random field perturbation. The correlation function and the Edwards-Anderson order parameter Q are discussed. For finite q only the phase with Q ≠ 0 is present. (Author) [pt

Exact solutions of the two-dimensional discrete nonlinear Schrodinger equation with saturable nonlinearity

DEFF Research Database (Denmark)

Khare, A.; Rasmussen, K. O.; Samuelsen, Mogens Rugholm

2010-01-01

We show that the two-dimensional, nonlinear Schrodinger lattice with a saturable nonlinearity admits periodic and pulse-like exact solutions. We establish the general formalism for the stability considerations of these solutions and give examples of stability diagrams. Finally, we show that the e...

The Semianalytical Solutions for Stiff Systems of Ordinary Differential Equations by Using Variational Iteration Method and Modified Variational Iteration Method with Comparison to Exact Solutions

Directory of Open Access Journals (Sweden)

Mehmet Tarik Atay

2013-01-01

Full Text Available The Variational Iteration Method (VIM and Modified Variational Iteration Method (MVIM are used to find solutions of systems of stiff ordinary differential equations for both linear and nonlinear problems. Some examples are given to illustrate the accuracy and effectiveness of these methods. We compare our results with exact results. In some studies related to stiff ordinary differential equations, problems were solved by Adomian Decomposition Method and VIM and Homotopy Perturbation Method. Comparisons with exact solutions reveal that the Variational Iteration Method (VIM and the Modified Variational Iteration Method (MVIM are easier to implement. In fact, these methods are promising methods for various systems of linear and nonlinear stiff ordinary differential equations. Furthermore, VIM, or in some cases MVIM, is giving exact solutions in linear cases and very satisfactory solutions when compared to exact solutions for nonlinear cases depending on the stiffness ratio of the stiff system to be solved.

Exact Solution of Mutator Model with Linear Fitness and Finite Genome Length

Science.gov (United States)

Saakian, David B.

2017-08-01

We considered the infinite population version of the mutator phenomenon in evolutionary dynamics, looking at the uni-directional mutations in the mutator-specific genes and linear selection. We solved exactly the model for the finite genome length case, looking at the quasispecies version of the phenomenon. We calculated the mutator probability both in the statics and dynamics. The exact solution is important for us because the mutator probability depends on the genome length in a highly non-trivial way.

The Multi-Wave Method for Exact Solutions of Nonlinear Partial Differential Equations

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Yusuf Pandir

2018-02-01

Full Text Available In this research, we use the multi-wave method to obtain new exact solutions for generalized forms of 5th order KdV equation and fth order KdV (fKdV equation with power law nonlinearity. Computations are performed with the help of the mathematics software Mathematica. Then, periodic wave solutions, bright soliton solutions and rational function solutions with free parameters are obtained by this approach. It is shown that this method is very useful and effective.

Exact solutions of a class of fractional Hamiltonian equations involving Caputo derivatives

Energy Technology Data Exchange (ETDEWEB)

Baleanu, Dumitru [Department of Mathematics and Computer Sciences, Faculty of Arts and Sciences, Cankaya University, Ankara 06530 (Turkey); Trujillo, Juan J [Departamento de Analisis Matematico, University of La Laguna, 38271 La Laguna, Tenerife (Spain)], E-mail: dumitru@cankaya.edu.tr, E-mail: JTrujill@ullmat.es, E-mail: baleanu@venus.nipne.ro

2009-11-15

The fractional Hamiltonian equations corresponding to the Lagrangians of constrained systems within Caputo derivatives are investigated. The fractional phase space is obtained and the exact solutions of some constrained systems are obtained.

Exact analytic solutions for Mikheyev-Smirnov-Wolfenstein level crossings

International Nuclear Information System (INIS)

Noetzold, D.

1987-01-01

An exact formula for the transition probability in level-crossing phenomena is derived for a general case, ranging from adiabatic to sudden crossings. This is done in the context of neutrino flavor oscillations for the Mikheyev-Smirnov-Wolfenstein (MSW) effect, where hitherto only numerical or approximate solutions were obtained. The matter density or level splitting is assumed to be governed by a hyperbolic-tangent function which, however, can change arbitrarily fast between two constant values. For example, in context of the MSW effect this furnishes a nice fit to the solar density determining the level crossing of solar neutrinos. In the quasiadiabatic limit the exact Landau-Zener factor can be read off, correcting some expressions obtained so far. Even in the opposite limit of a sudden level crossing a conversion is found, which can have far-reaching consequences for neutrino detection on Earth

Some exact solutions to the potential Kadomtsev-Petviashvili equation and to a system of shallow water wave equations

International Nuclear Information System (INIS)

Inan, Ibrahim E.; Kaya, Dogan

2006-01-01

In this Letter by considering an improved tanh function method, we found some exact solutions of the potential Kadomtsev-Petviashvili equation. Some exact solutions of the system of the shallow water wave equation were also found

Exact solution of the Schroedinger equation with the spin-boson Hamiltonian

International Nuclear Information System (INIS)

Gardas, Bartlomiej

2011-01-01

We address the problem of obtaining the exact reduced dynamics of the spin-half (qubit) immersed within the bosonic bath (environment). An exact solution of the Schroedinger equation with the paradigmatic spin-boson Hamiltonian is obtained. We believe that this result is a major step ahead and may ultimately contribute to the complete resolution of the problem in question. We also construct the constant of motion for the spin-boson system. In contrast to the standard techniques available within the framework of the open quantum systems theory, our analysis is based on the theory of block operator matrices.

New Generalized Hyperbolic Functions to Find New Exact Solutions of the Nonlinear Partial Differential Equations

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Yusuf Pandir

2013-01-01

Full Text Available We firstly give some new functions called generalized hyperbolic functions. By the using of the generalized hyperbolic functions, new kinds of transformations are defined to discover the exact approximate solutions of nonlinear partial differential equations. Based on the generalized hyperbolic function transformation of the generalized KdV equation and the coupled equal width wave equations (CEWE, we find new exact solutions of two equations and analyze the properties of them by taking different parameter values of the generalized hyperbolic functions. We think that these solutions are very important to explain some physical phenomena.

Orbifolds and Exact Solutions of Strongly-Coupled Matrix Models

Science.gov (United States)

Córdova, Clay; Heidenreich, Ben; Popolitov, Alexandr; Shakirov, Shamil

2018-02-01

We find an exact solution to strongly-coupled matrix models with a single-trace monomial potential. Our solution yields closed form expressions for the partition function as well as averages of Schur functions. The results are fully factorized into a product of terms linear in the rank of the matrix and the parameters of the model. We extend our formulas to include both logarithmic and finite-difference deformations, thereby generalizing the celebrated Selberg and Kadell integrals. We conjecture a formula for correlators of two Schur functions in these models, and explain how our results follow from a general orbifold-like procedure that can be applied to any one-matrix model with a single-trace potential.

Some exact solutions with torsion in 5D Einstein-Gauss-Bonnet gravity

International Nuclear Information System (INIS)

Canfora, F.; Giacomini, A.; Willison, S.

2007-01-01

Exact solutions with torsion in Einstein-Gauss-Bonnet gravity are derived. These solutions have a cross product structure of two constant curvature manifolds. The equations of motion give a relation for the coupling constants of the theory in order to have solutions with nontrivial torsion. This relation is not the Chern-Simons combination. One of the solutions has an AdS 2 xS 3 structure and is so the purely gravitational analogue of the Bertotti-Robinson space-time where the torsion can be seen as the dual of the covariantly constant electromagnetic field

The fractional coupled KdV equations: Exact solutions and white noise functional approach

International Nuclear Information System (INIS)

Ghany, Hossam A.; El Bab, A. S. Okb; Zabel, A. M.; Hyder, Abd-Allah

2013-01-01

Variable coefficients and Wick-type stochastic fractional coupled KdV equations are investigated. By using the modified fractional sub-equation method, Hermite transform, and white noise theory the exact travelling wave solutions and white noise functional solutions are obtained, including the generalized exponential, hyperbolic, and trigonometric types. (general)

Exact, E = 0, classical and quantum solutions for general power-law oscillators

International Nuclear Information System (INIS)

Nieto, M.M.; Daboul, J.

1994-01-01

For zero energy, E = 0, we derive exact, classical and quantum solutions for all power-law oscillators with potentials V(r) = -γ/r ν , γ > 0 and -∞ 0 (t))] 1/μ , with μ = ν/2 - 1 ≠ 0. For ν > 2, the orbits are bound and go through the origin. We calculate the periods and precessions of these bound orbits, and graph a number of specific examples. The unbound orbits are also discussed in detail. Quantum mechanically, this system is also exactly solvable. We find that when ν > 2 the solutions are normalizable (bound), as in the classical case. Also, there are normalizable discrete, yet unbound, state which correspond to unbound classical particles which reach infinity in a finite time. These and other interesting comparisons to the classical system will be discussed

Hydrodynamics beyond Navier-Stokes: exact solution to the lattice Boltzmann hierarchy.

Science.gov (United States)

Ansumali, S; Karlin, I V; Arcidiacono, S; Abbas, A; Prasianakis, N I

2007-03-23

The exact solution to the hierarchy of nonlinear lattice Boltzmann (LB) kinetic equations in the stationary planar Couette flow is found at nonvanishing Knudsen numbers. A new method of solving LB kinetic equations which combines the method of moments with boundary conditions for populations enables us to derive closed-form solutions for all higher-order moments. A convergence of results suggests that the LB hierarchy with larger velocity sets is the novel way to approximate kinetic theory.

A transformed rational function method and exact solutions to the 3+1 dimensional Jimbo-Miwa equation

International Nuclear Information System (INIS)

Ma Wenxiu; Lee, J.-H.

2009-01-01

A direct approach to exact solutions of nonlinear partial differential equations is proposed, by using rational function transformations. The new method provides a more systematical and convenient handling of the solution process of nonlinear equations, unifying the tanh-function type methods, the homogeneous balance method, the exp-function method, the mapping method, and the F-expansion type methods. Its key point is to search for rational solutions to variable-coefficient ordinary differential equations transformed from given partial differential equations. As an application, the construction problem of exact solutions to the 3+1 dimensional Jimbo-Miwa equation is treated, together with a Baecklund transformation.

A Large Class of Exact Solutions to the One-Dimensional Schrodinger Equation

Science.gov (United States)

Karaoglu, Bekir

2007-01-01

A remarkable property of a large class of functions is exploited to generate exact solutions to the one-dimensional Schrodinger equation. The method is simple and easy to implement. (Contains 1 table and 1 figure.)

Exact solutions and critical chaos in dilaton gravity with a boundary

Energy Technology Data Exchange (ETDEWEB)

Fitkevich, Maxim [Institute for Nuclear Research of the Russian Academy of Sciences,60th October Anniversary Prospect 7a, Moscow 117312 (Russian Federation); Moscow Institute of Physics and Technology,Institutskii per. 9, Dolgoprudny 141700, Moscow Region (Russian Federation); Levkov, Dmitry [Institute for Nuclear Research of the Russian Academy of Sciences,60th October Anniversary Prospect 7a, Moscow 117312 (Russian Federation); Zenkevich, Yegor [Dipartimento di Fisica, Università di Milano-Bicocca,Piazza della Scienza 3, I-20126 Milano (Italy); INFN, sezione di Milano-Bicocca,I-20126 Milano (Italy); National Research Nuclear University MEPhI,Moscow 115409 (Russian Federation)

2017-04-19

We consider (1+1)-dimensional dilaton gravity with a reflecting dynamical boundary. The boundary cuts off the region of strong coupling and makes our model causally similar to the spherically-symmetric sector of multidimensional gravity. We demonstrate that this model is exactly solvable at the classical level and possesses an on-shell SL(2, ℝ) symmetry. After introducing general classical solution of the model, we study a large subset of soliton solutions. The latter describe reflection of matter waves off the boundary at low energies and formation of black holes at energies above critical. They can be related to the eigenstates of the auxiliary integrable system, the Gaudin spin chain. We argue that despite being exactly solvable, the model in the critical regime, i.e. at the verge of black hole formation, displays dynamical instabilities specific to chaotic systems. We believe that this model will be useful for studying black holes and gravitational scattering.

Exact solution of a quasi-one-dimensional model with long range interaction (coupled tomonaga chains)

International Nuclear Information System (INIS)

Nguyen Minh Khue; Solyom, J.

1980-03-01

The novel method proposed by one of the authors to calculate exactly the response functions of the one-dimensional Tomonaga-model is described in more detail. The method is generalized for the case of a system of coupled chains where both the interchain and interchain interactions have forward scattering components only. The model does not show real phase transition at any finite temperature indicating that the interchain backward scattering or hopping is needed to have an ordering of the chains at finite temperature. (author)

Exact solution in the cosmological chaotic inflation model with induced gravity

International Nuclear Information System (INIS)

Wang Wenfu

2004-01-01

We present a new, exact solution in the cosmological chaotic inflation model with induced gravity. The spectral index of the scalar density fluctuations, n s , is computed, and is consistent with the analyses of BOOMERANG data. The effective cosmological constant Λ eff tends to zero when inflation ends

Exact Solutions of the Hierarchical Korteweg-de Vries Equation of Micro structured Granular Materials

International Nuclear Information System (INIS)

Abourabia, A.M.; El-Danaf, T.S.; Morad, A.M.

2008-01-01

The problem under consideration are related to wave propagation in micro structured materials, characterized by higher-order nonlinear and higher-order dispersive effects; particularly, the wave propagation in dilatant granular materials. In the present paper the model equation is solved analytically by exact method called Jacobi elliptic method. The types of solutions are defined and discussed over a wide range of material parameters (two dispersion parameters and one microstructure parameter). The dispersion properties and the relation between group and phase velocities of the model equation are studied. The diagrams are drawn to illustrate the physical properties of the exact solutions

EDISON-WMW: Exact Dynamic Programing Solution of the Wilcoxon–Mann–Whitney Test

Directory of Open Access Journals (Sweden)

Alexander Marx

2016-02-01

Full Text Available In many research disciplines, hypothesis tests are applied to evaluate whether findings are statistically significant or could be explained by chance. The Wilcoxon–Mann–Whitney (WMW test is among the most popular hypothesis tests in medicine and life science to analyze if two groups of samples are equally distributed. This nonparametric statistical homogeneity test is commonly applied in molecular diagnosis. Generally, the solution of the WMW test takes a high combinatorial effort for large sample cohorts containing a significant number of ties. Hence, P value is frequently approximated by a normal distribution. We developed EDISON-WMW, a new approach to calculate the exact permutation of the two-tailed unpaired WMW test without any corrections required and allowing for ties. The method relies on dynamic programing to solve the combinatorial problem of the WMW test efficiently. Beyond a straightforward implementation of the algorithm, we presented different optimization strategies and developed a parallel solution. Using our program, the exact P value for large cohorts containing more than 1000 samples with ties can be calculated within minutes. We demonstrate the performance of this novel approach on randomly-generated data, benchmark it against 13 other commonly-applied approaches and moreover evaluate molecular biomarkers for lung carcinoma and chronic obstructive pulmonary disease (COPD. We found that approximated P values were generally higher than the exact solution provided by EDISON-WMW. Importantly, the algorithm can also be applied to high-throughput omics datasets, where hundreds or thousands of features are included. To provide easy access to the multi-threaded version of EDISON-WMW, a web-based solution of our algorithm is freely available at http://www.ccb.uni-saarland.de/software/wtest/.

Painlevé analysis and exact solutions for the Belousov–Zhabotinskii reaction–diffusion system

International Nuclear Information System (INIS)

Kudryashov, Nikolay A.; Zakharchenko, Anastasia S.

2014-01-01

A system of equations for description of the Belousov–Zhabotinskii chemical reaction is considered. The Painlevé analysis of this reaction–diffusion system is studied. Exact traveling wave solutions of the system for the Belousov–Zhabotinskii reaction are found. Periodic solutions expressed in terms of the Weierstrass elliptic function are also given

Theory of quasi-Chaplygin unstable media and evolutionary principle for selecting spontaneous solutions

International Nuclear Information System (INIS)

Zhdanov, S.K.; Trubnikov, B.A.; Institut Atomnoi Energii, Moscow, USSR)

1986-01-01

A one-dimensional ideal gas with negative compressibility described by quasi-Chaplygin equations is discussed. Its reduction to a Laplace equation is shown, and an evolutionary principle for selecting spontaneous solutions is summarized. Three extremely simple spontaneous solutions are obtained along with multidimensional self-similar solutions. The Buneman instability in a plasma is considered as an example. 17 references

Homoclinic and quasi-homoclinic solutions for damped differential equations

Directory of Open Access Journals (Sweden)

Chuan-Fang Zhang

2015-01-01

Full Text Available We study the existence and multiplicity of homoclinic solutions for the second-order damped differential equation $$ \\ddot{u}+c\\dot{u}-L(tu+W_u(t,u=0, $$ where L(t and W(t,u are neither autonomous nor periodic in t. Under certain assumptions on L and W, we obtain infinitely many homoclinic solutions when the nonlinearity W(t,u is sub-quadratic or super-quadratic by using critical point theorems. Some recent results in the literature are generalized, and the open problem proposed by Zhang and Yuan is solved. In addition, with the help of the Nehari manifold, we consider the case where W(t,u is indefinite and prove the existence of at least one nontrivial quasi-homoclinic solution.

Exact Analytical Solutions in Three-Body Problems and Model of Neutrino Generator

Directory of Open Access Journals (Sweden)

Takibayev N.Zh.

2010-04-01

Full Text Available Exact analytic solutions are obtained in three-body problem for the scattering of light particle on the subsystem of two fixed centers in the case when pair potentials have a separable form. Solutions show an appearance of new resonance states and dependence of resonance energy and width on distance between two fixed centers. The approach of exact analytical solutions is expanded to the cases when two-body scattering amplitudes have the Breit-Wigner’s form and employed for description of neutron resonance scattering on subsystem of two heavy nuclei fixed in nodes of crystalline lattice. It is shown that some resonance states have widths close to zero at the certain values of distance between two heavy scatterer centers, this gives the possibility of transitions between states. One of these transitions between three-body resonance states could be connected with process of electron capture by proton with formation of neutron and emission of neutrino. This exoenergic process leading to the cooling of star without nuclear reactions is discussed.

Methods for constructing exact solutions of partial differential equations mathematical and analytical techniques with applications to engineering

CERN Document Server

Meleshko, Sergey V

2005-01-01

Differential equations, especially nonlinear, present the most effective way for describing complex physical processes. Methods for constructing exact solutions of differential equations play an important role in applied mathematics and mechanics. This book aims to provide scientists, engineers and students with an easy-to-follow, but comprehensive, description of the methods for constructing exact solutions of differential equations.

Strong pairing approximation in comparison with the exact solutions to the pairing Hamiltonian

Directory of Open Access Journals (Sweden)

Lunyov A.V.

2016-01-01

Full Text Available Results of the Strong Pairing Approximation (SPA as a method with the exact particle number conservation are compared with those of the quasiparticle method (QM. It is shown that SPA comes to the same equations as QM for the gap parameter, chemical potential and one- and two-quasiparticle states. Calculations are performed for 14864Gd84 as an example, and compared with the exact solutions to the pairing Hamiltonian.

Exact travelling wave solutions of the (3+1)-dimensional mKdV-ZK ...

Indian Academy of Sciences (India)

In this paper, the new generalized (′/)-expansion method is executed to find the travelling wave solutions of the (3+1)-dimensional mKdV-ZK equation and the (1+1)-dimensional compound KdVB equation. The efficiency of this method for finding exact and travelling wave solutions has been demonstrated. It is shown ...

Exact periodic solutions of the sixth-order generalized Boussinesq equation

International Nuclear Information System (INIS)

Kamenov, O Y

2009-01-01

This paper examines a class of nonlinear sixth-order generalized Boussinesq-like equations (SGBE): u tt = u xx + 3(u 2 ) xx + u xxxx + αu xxxxxx , α in R, depending on the positive parameter α. Hirota's bilinear transformation method is applied to the above class of non-integrable equations and exact periodic solutions have been obtained. The results confirmed the well-known nonlinear superposition principle.

Exact Solutions of the Space Time Fractional Symmetric Regularized Long Wave Equation Using Different Methods

Directory of Open Access Journals (Sweden)

Özkan Güner

2014-01-01

Full Text Available We apply the functional variable method, exp-function method, and (G′/G-expansion method to establish the exact solutions of the nonlinear fractional partial differential equation (NLFPDE in the sense of the modified Riemann-Liouville derivative. As a result, some new exact solutions for them are obtained. The results show that these methods are very effective and powerful mathematical tools for solving nonlinear fractional equations arising in mathematical physics. As a result, these methods can also be applied to other nonlinear fractional differential equations.

Exact self-similar solutions for the magnetized Noh Z pinch problem

International Nuclear Information System (INIS)

Velikovich, A. L.; Giuliani, J. L.; Thornhill, J. W.; Zalesak, S. T.; Gardiner, T. A.

2012-01-01

A self-similar solution is derived for a radially imploding cylindrical plasma with an embedded, azimuthal magnetic field. The plasma stagnates through a strong, outward propagating shock wave of constant velocity. This analysis is an extension of the classic Noh gasdynamics problem to its ideal magnetohydrodynamics (MHD) counterpart. The present exact solution is especially suitable as a test for MHD codes designed to simulate linear Z pinches. To demonstrate the application of the new solution to code verification, simulation results from the cylindrical R-Z version of Mach2 and the 3D Cartesian code Athena are compared against the analytic solution. Alternative routines from the default ones in Athena lead to significant improvement of the results, thereby demonstrating the utility of the self-similar solution for verification.

Exact Solutions of a High-Order Nonlinear Wave Equation of Korteweg-de Vries Type under Newly Solvable Conditions

Directory of Open Access Journals (Sweden)

Weiguo Rui

2014-01-01

Full Text Available By using the integral bifurcation method together with factoring technique, we study a water wave model, a high-order nonlinear wave equation of KdV type under some newly solvable conditions. Based on our previous research works, some exact traveling wave solutions such as broken-soliton solutions, periodic wave solutions of blow-up type, smooth solitary wave solutions, and nonsmooth peakon solutions within more extensive parameter ranges are obtained. In particular, a series of smooth solitary wave solutions and nonsmooth peakon solutions are obtained. In order to show the properties of these exact solutions visually, we plot the graphs of some representative traveling wave solutions.

The exact solution of self-consistent equations in the scanning near-field optic microscopy problem

DEFF Research Database (Denmark)

Lozovski, Valeri; Bozhevolnyi, Sergey I.

1999-01-01

The macroscopic approach that allows one to obtain an exact solution of the self-consistent equation of the Lippmann-Schwinger type is developed. The main idea of our method consist in usage of diagram technque for exact summation of the infinite series corresponding to the iteration procedure fo...

Exactly complete solutions of the Schroedinger equation with a spherically harmonic oscillatory ring-shaped potential

International Nuclear Information System (INIS)

Zhang Mincang; Sun Guohua; Dong Shihai

2010-01-01

A spherically harmonic oscillatory ring-shaped potential is proposed and its exactly complete solutions are presented by the Nikiforov-Uvarov method. The effect of the angle-dependent part on the radial solutions is discussed.

New exact solution for the exterior gravitational field of a charged spinning mass

International Nuclear Information System (INIS)

Chamorro, A.; Manko, V.S.; Denisova, T.E.

1991-01-01

An exact asymptotically flat solution of the Einstein-Maxwell equations describing the exterior gravitational field of a charged rotating axisymmetric mass possessing an arbitrary set of multipole moments is presented explicitly

Boundary Value Problems for a Super-Sublinear Asymmetric Oscillator: The Exact Number of Solutions

Directory of Open Access Journals (Sweden)

Armands Gritsans

2013-01-01

Full Text Available Properties of asymmetric oscillator described by the equation (i, where and , are studied. A set of such that the problem (i, (ii, and (iii have a nontrivial solution, is called α-spectrum. We give full description of α-spectra in terms of solution sets and solution surfaces. The exact number of nontrivial solutions of the two-parameter Dirichlet boundary value problem (i, and (ii is given.

On symmetries and exact solutions of the Einstein–Maxwell field equations via the symmetry approach

International Nuclear Information System (INIS)

Kaur, Lakhveer; Gupta, R K

2013-01-01

Using the Lie symmetry approach, we have examined herein the system of partial differential equations corresponding to the Einstein–Maxwell equations for a static axially symmetric spacetime. The method used reduces the system of partial differential equations to a system of ordinary differential equations according to the Lie symmetry admitted. In particular, we found the relevant system of ordinary differential equations is all optimal subgroups. The system of ordinary differential equations is further solved in general to obtain exact solutions. Several new physically important families of exact solutions are derived. (paper)

Explicit and exact nontraveling wave solutions of the (3+1)-dimensional potential Yu-Toda-Sasa-Fukuyama equation

Science.gov (United States)

Yuan, Na

2018-04-01

With the aid of the symbolic computation, we present an improved ( G ‧ / G ) -expansion method, which can be applied to seek more types of exact solutions for certain nonlinear evolution equations. In illustration, we choose the (3 + 1)-dimensional potential Yu-Toda-Sasa-Fukuyama equation to demonstrate the validity and advantages of the method. As a result, abundant explicit and exact nontraveling wave solutions are obtained including two solitary waves solutions, nontraveling wave solutions and dromion soliton solutions. Some particular localized excitations and the interactions between two solitary waves are researched. The method can be also applied to other nonlinear partial differential equations.

Exact solutions to the supply chain equations for arbitrary, time-dependent demands

DEFF Research Database (Denmark)

Warburton, Roger D.H.; Hodgson, J.P.E.; Nielsen, Erland Hejn

2014-01-01

, so users can determine the inventory behavior to any desired precision. To illustrate, we solve the equations for a non-linear, quadratic time-dependence in the demand. For practical use, only a few terms in the series are required, a proposition illustrated by the For All Practical Purposes (FAPP......We study the impact on inventory of an unexpected, non-linear, time-dependent demand and present the exact solutions over time to the supply chain equations without requiring any approximations. We begin by imposing a boundary condition of stability at infinity, from which we derive expressions...... for the estimated demand and the target work in progress when the demand is time-dependent. The resulting inventory equation is solved in terms of the Lambert modes with all of the demand non-linearities confined to the pre-shape function. The series solution is exact, and all terms are reasonably easy to calculate...

A Monte Carlo implementation of the predictor-corrector Quasi-Static method

International Nuclear Information System (INIS)

Hackemack, M. W.; Ragusa, J. C.; Griesheimer, D. P.; Pounders, J. M.

2013-01-01

The Quasi-Static method (QS) is a useful tool for solving reactor transients since it allows for larger time steps when updating neutron distributions. Because of the beneficial attributes of Monte Carlo (MC) methods (exact geometries and continuous energy treatment), it is desirable to develop a MC implementation for the QS method. In this work, the latest version of the QS method known as the Predictor-Corrector Quasi-Static method is implemented. Experiments utilizing two energy-groups provide results that show good agreement with analytical and reference solutions. The method as presented can easily be implemented in any continuous energy, arbitrary geometry, MC code. (authors)

Some new exact solutions of Jacobian elliptic function about the generalized Boussinesq equation and Boussinesq-Burgers equation

International Nuclear Information System (INIS)

Zhang Liang; Zhang Lifeng; Li Chongyin

2008-01-01

By using the modified mapping method, we find some new exact solutions of the generalized Boussinesq equation and the Boussinesq-Burgers equation. The solutions obtained in this paper include Jacobian elliptic function solutions, combined Jacobian elliptic function solutions, soliton solutions, triangular function solutions

Solutions for confluent and double-confluent Heun equations and some applications

Energy Technology Data Exchange (ETDEWEB)

El-Jaick, Lea Jaccoud; Figueiredo, Bartolomeu D.B. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)

2008-07-01

This paper examines some solutions for confluent and double-confluent Heun equations and their applications to the Schroedinger equation with quasi-exactly solvable potentials. In the first place, we review two Leaver's solutions in series of regular and irregular confluent hypergeometric functions for the confluent equation [E. W. Leaver, J. Math. Phys. 27, 1238 (1986)] and introduce an additional expansion in series of irregular confluent hypergeometric functions. Then, we find the conditions under which one of these solutions can be written as a linear combination of the others. In the second place, by means of limiting procedures we generate solutions for the double-confluent equation as well as for special limits of both the confluent and double-confluent equations. In the third place, solutions of the Heun equations are used to solve the one-dimensional Schroedinger equation for quasi-exactly solvable potentials. We consider a symmetric and an asymmetric double-Morse potentials which appear in the theory of quantum spin systems [O. B. Zaslavskii and V. V. Ulyanov, Sov. Phys. JETP 60, 991 (1984)], a bottomless volcano-type potential which gives degenerate eigenstates [S. Kar and R. R. Parwani, Europhys. Lett., 80, 30004 (2007)], and a potential which leads to quasi normal modes, that is, to solutions presenting complex energies [H. T. Cho and C. L. Ho, J. Phys. A: Math. Theor. 40, 1325 (2007)]. (author)

Solutions for confluent and double-confluent Heun equations and some applications

International Nuclear Information System (INIS)

El-Jaick, Lea Jaccoud; Figueiredo, Bartolomeu D.B.

2008-01-01

This paper examines some solutions for confluent and double-confluent Heun equations and their applications to the Schroedinger equation with quasi-exactly solvable potentials. In the first place, we review two Leaver's solutions in series of regular and irregular confluent hypergeometric functions for the confluent equation [E. W. Leaver, J. Math. Phys. 27, 1238 (1986)] and introduce an additional expansion in series of irregular confluent hypergeometric functions. Then, we find the conditions under which one of these solutions can be written as a linear combination of the others. In the second place, by means of limiting procedures we generate solutions for the double-confluent equation as well as for special limits of both the confluent and double-confluent equations. In the third place, solutions of the Heun equations are used to solve the one-dimensional Schroedinger equation for quasi-exactly solvable potentials. We consider a symmetric and an asymmetric double-Morse potentials which appear in the theory of quantum spin systems [O. B. Zaslavskii and V. V. Ulyanov, Sov. Phys. JETP 60, 991 (1984)], a bottomless volcano-type potential which gives degenerate eigenstates [S. Kar and R. R. Parwani, Europhys. Lett., 80, 30004 (2007)], and a potential which leads to quasi normal modes, that is, to solutions presenting complex energies [H. T. Cho and C. L. Ho, J. Phys. A: Math. Theor. 40, 1325 (2007)]. (author)

Exact solution of unsteady flow generated by sinusoidal pressure gradient in a capillary tube

Directory of Open Access Journals (Sweden)

M. Abdulhameed

2015-12-01

Full Text Available In this paper, the mathematical modeling of unsteady second grade fluid in a capillary tube with sinusoidal pressure gradient is developed with non-homogenous boundary conditions. Exact analytical solutions for the velocity profiles have been obtained in explicit forms. These solutions are written as the sum of the steady and transient solutions for small and large times. For growing times, the starting solution reduces to the well-known periodic solution that coincides with the corresponding solution of a Newtonian fluid. Graphs representing the solutions are discussed.

An analytical method for solving exact solutions of a nonlinear evolution equation describing the dynamics of ionic currents along microtubules

Directory of Open Access Journals (Sweden)

Md. Nur Alam

2017-11-01

Full Text Available In this article, a variety of solitary wave solutions are observed for microtubules (MTs. We approach the problem by treating the solutions as nonlinear RLC transmission lines and then find exact solutions of Nonlinear Evolution Equations (NLEEs involving parameters of special interest in nanobiosciences and biophysics. We determine hyperbolic, trigonometric, rational and exponential function solutions and obtain soliton-like pulse solutions for these equations. A comparative study against other methods demonstrates the validity of the technique that we developed and demonstrates that our method provides additional solutions. Finally, using suitable parameter values, we plot 2D and 3D graphics of the exact solutions that we observed using our method. Keywords: Analytical method, Exact solutions, Nonlinear evolution equations (NLEEs of microtubules, Nonlinear RLC transmission lines

A new generalized exponential rational function method to find exact special solutions for the resonance nonlinear Schrödinger equation

Science.gov (United States)

Ghanbari, Behzad; Inc, Mustafa

2018-04-01

The present paper suggests a novel technique to acquire exact solutions of nonlinear partial differential equations. The main idea of the method is to generalize the exponential rational function method. In order to examine the ability of the method, we consider the resonant nonlinear Schrödinger equation (R-NLSE). Many variants of exact soliton solutions for the equation are derived by the proposed method. Physical interpretations of some obtained solutions is also included. One can easily conclude that the new proposed method is very efficient and finds the exact solutions of the equation in a relatively easy way.

Some Considerations on the Fundamentals of Chemical Kinetics: Steady State, Quasi-Equilibrium, and Transition State Theory

Science.gov (United States)

Perez-Benito, Joaquin F.

2017-01-01

The elementary reaction sequence A ? I ? Products is the simplest mechanism for which the steady-state and quasi-equilibrium kinetic approximations can be applied. The exact integrated solutions for this chemical system allow inferring the conditions that must fulfill the rate constants for the different approximations to hold. A graphical…

New Exact Solutions for New Model Nonlinear Partial Differential Equation

OpenAIRE

Maher, A.; El-Hawary, H. M.; Al-Amry, M. S.

2013-01-01

In this paper we propose a new form of Padé-II equation, namely, a combined Padé-II and modified Padé-II equation. The mapping method is a promising method to solve nonlinear evaluation equations. Therefore, we apply it, to solve the combined Padé-II and modified Padé-II equation. Exact travelling wave solutions are obtained and expressed in terms of hyperbolic functions, trigonometric functions, rational functions, and elliptic functions.

Exact solution of the three-boson problem at vanishing energy

International Nuclear Information System (INIS)

Mora, Ch.; Gogolin, A.O.; Egger, R.

2011-01-01

A zero-range approach is used to model resonant two-body interactions between three identical bosons. A dimensionless phase parameterizes the three-body boundary condition while the scattering length enters the Bethe-Peierls boundary condition. The model is solved exactly at zero energy for any value of the scattering length, positive or negative. From this solution, an analytical expression for the rate of three-body recombination to the universal shallow dimer is extracted. (authors)

Exact periodic solutions of the sixth-order generalized Boussinesq equation

Energy Technology Data Exchange (ETDEWEB)

Kamenov, O Y [Department of Applied Mathematics and Informatics, Technical University of Sofia, PO Box 384, 1000 Sofia (Bulgaria)], E-mail: okam@abv.bg

2009-09-18

This paper examines a class of nonlinear sixth-order generalized Boussinesq-like equations (SGBE): u{sub tt} = u{sub xx} + 3(u{sup 2}){sub xx} + u{sub xxxx} + {alpha}u{sub xxxxxx}, {alpha} in R, depending on the positive parameter {alpha}. Hirota's bilinear transformation method is applied to the above class of non-integrable equations and exact periodic solutions have been obtained. The results confirmed the well-known nonlinear superposition principle.

Exact partial solution to the steady-state, compressible fluid flow problems of jet formation and jet penetration

International Nuclear Information System (INIS)

Karpp, R.R.

1980-10-01

This report treats analytically the problem of the symmetric impact of two compressible fluid streams. The flow is assumed to be steady, plane, inviscid, and subsonic and that the compressible fluid is of the Chaplygin (tangent gas) type. In the analysis, the governing equations are first transformed to the hodograph plane where an exact, closed-form solution is obtained by standard techniques. The distributions of fluid properties along the plane of symmetry as well as the shapes of the boundary streamlines are exactly determined by transforming the solution back to the physical plane. The problem of a compressible fluid jet penetrating into an infinite target of similar material is also exactly solved by considering a limiting case of this solution. This new compressible flow solution reduces to the classical result of incompressible flow theory when the sound speed of the fluid is allowed to approach infinity. Several illustrations of the differences between compressible and incompressible flows of the type considered are presented

Modified quasi-boundary value method for Cauchy problems of elliptic equations with variable coefficients

Directory of Open Access Journals (Sweden)

Hongwu Zhang

2011-08-01

Full Text Available In this article, we study a Cauchy problem for an elliptic equation with variable coefficients. It is well-known that such a problem is severely ill-posed; i.e., the solution does not depend continuously on the Cauchy data. We propose a modified quasi-boundary value regularization method to solve it. Convergence estimates are established under two a priori assumptions on the exact solution. A numerical example is given to illustrate our proposed method.

Canonical reduction of self-dual Yang-Mills equations to Fitzhugh-Nagumo equation and exact solutions

International Nuclear Information System (INIS)

Sayed, S.M.; Gharib, G.M.

2009-01-01

The (constrained) canonical reduction of four-dimensional self-dual Yang-Mills theory to two-dimensional Fitzhugh-Nagumo and the real Newell-Whitehead equations are considered. On the other hand, other methods and transformations are developed to obtain exact solutions for the original two-dimensional Fitzhugh-Nagumo and Newell-Whitehead equations. The corresponding gauge potential A μ and the gauge field strengths F μν are also obtained. New explicit and exact traveling wave and solitary solutions (for Fitzhugh-Nagumo and Newell-Whitehead equations) are obtained by using an improved sine-cosine method and the Wu's elimination method with the aid of Mathematica.

Exact Solution of Space-Time Fractional Coupled EW and Coupled MEW Equations Using Modified Kudryashov Method

International Nuclear Information System (INIS)

Raslan, K. R.; Ali, Khalid K.; EL-Danaf, Talaat S.

2017-01-01

In the present paper, we established a traveling wave solution by using modified Kudryashov method for the space-time fractional nonlinear partial differential equations. The method is used to obtain the exact solutions for different types of the space-time fractional nonlinear partial differential equations such as, the space-time fractional coupled equal width wave equation (CEWE) and the space-time fractional coupled modified equal width wave equation (CMEW), which are the important soliton equations. Both equations are reduced to ordinary differential equations by the use of fractional complex transform and properties of modified Riemann–Liouville derivative. We plot the exact solutions for these equations at different time levels. (paper)

On symmetry reduction and exact solutions of the linear one-dimensional Schroedinger equation

International Nuclear Information System (INIS)

Barannik, L.L.

1996-01-01

Symmetry reduction of the Schroedinger equation with potential is carried out on subalgebras of the Lie algebra which is the direct sum of the special Galilei algebra and one-dimensional algebra. Some new exact solutions are obtained

On reduction and exact solutions of nonlinear many-dimensional Schroedinger equations

International Nuclear Information System (INIS)

Barannik, A.F.; Marchenko, V.A.; Fushchich, V.I.

1991-01-01

With the help of the canonical decomposition of an arbitrary subalgebra of the orthogonal algebra AO(n) the rank n and n-1 maximal subalgebras of the extended isochronous Galileo algebra, the rank n maximal subalgebras of the generalized extended classical Galileo algebra AG(a,n) the extended special Galileo algebra AG(2,n) and the extended whole Galileo algebra AG(3,n) are described. By using the rank n subalgebras, ansatze reducing the many dimensional Schroedinger equations to ordinary differential equations is found. With the help of the reduced equation solutions exact solutions of the Schroedinger equation are considered

Exact Solutions of a Fractional-Type Differential-Difference Equation Related to Discrete MKdV Equation

International Nuclear Information System (INIS)

Aslan İsmail

2014-01-01

The extended simplest equation method is used to solve exactly a new differential-difference equation of fractional-type, proposed by Narita [J. Math. Anal. Appl. 381 (2011) 963] quite recently, related to the discrete MKdV equation. It is shown that the model supports three types of exact solutions with arbitrary parameters: hyperbolic, trigonometric and rational, which have not been reported before. (general)

Exact solitary wave solutions for some nonlinear evolution equations via Exp-function method

International Nuclear Information System (INIS)

Ebaid, A.

2007-01-01

Based on the Exp-function method, exact solutions for some nonlinear evolution equations are obtained. The KdV equation, Burgers' equation and the combined KdV-mKdV equation are chosen to illustrate the effectiveness of the method

Trial function method and exact solutions to the generalized nonlinear Schrödinger equation with time-dependent coefficient

International Nuclear Information System (INIS)

Cao Rui; Zhang Jian

2013-01-01

In this paper, the trial function method is extended to study the generalized nonlinear Schrödinger equation with time-dependent coefficients. On the basis of a generalized traveling wave transformation and a trial function, we investigate the exact envelope traveling wave solutions of the generalized nonlinear Schrödinger equation with time-dependent coefficients. Taking advantage of solutions to trial function, we successfully obtain exact solutions for the generalized nonlinear Schrödinger equation with time-dependent coefficients under constraint conditions. (general)

Exact solutions to a class of nonlinear Schrödinger-type equations

Indian Academy of Sciences (India)

A class of nonlinear Schrödinger-type equations, including the Rangwala–Rao equation, the Gerdjikov–Ivanov equation, the Chen–Lee–Lin equation and the Ablowitz–Ramani–Segur equation are investigated, and the exact solutions are derived with the aid of the homogeneous balance principle, and a set of subsidiary ...

Stability of exact solutions describing two-layer flows with evaporation at the interface

Energy Technology Data Exchange (ETDEWEB)

Bekezhanova, V B [Institute of Computational Modelling SB RAS, Akademgorodok, 50/44, Krasnoyarsk, 660036 (Russian Federation); Goncharova, O N, E-mail: bekezhanova@mail.ru, E-mail: gon@math.asu.ru [Altai State University, Lenina 61, Barnaul, 656049 (Russian Federation)

2016-12-15

A new exact solution of the equations of free convection has been constructed in the framework of the Oberbeck–Boussinesq approximation of the Navier–Stokes equations. The solution describes the joint flow of an evaporating viscous heat-conducting liquid and gas-vapor mixture in a horizontal channel. In the gas phase the Dufour and Soret effects are taken into account. The consideration of the exact solution allows one to describe different classes of flows depending on the values of the problem parameters and boundary conditions for the vapor concentration. A classification of solutions and results of the solution analysis are presented. The effects of the external disturbing influences (of the liquid flow rates and longitudinal gradients of temperature on the channel walls) on the stability characteristics have been numerically studied for the system HFE7100-nitrogen in the common case, when the longitudinal temperature gradients on the boundaries of the channel are not equal. In the system both monotonic and oscillatory modes can be formed, which damp or grow depending on the values of the initial perturbations, flow rates and temperature gradients. Hydrodynamic perturbations are most dangerous under large gas flow rates. The increasing oscillatory perturbations are developed due to the thermocapillary effect under large longitudinal gradients of temperature. The typical forms of the disturbances are shown. (paper)

Canonical reduction of self-dual Yang-Mills equations to Fitzhugh-Nagumo equation and exact solutions

Energy Technology Data Exchange (ETDEWEB)

Sayed, S.M. [Mathematics Department, Faculty of Science, Beni-Suef University, Beni-Suef (Egypt); Mathematics Department, P.O. Box 1144, Tabouk Teacher College, Ministry of Education (Saudi Arabia)], E-mail: eaashour@lycos.com; Gharib, G.M. [Mathematics Department, P.O. Box 1144, Tabouk Teacher College, Ministry of Education (Saudi Arabia)

2009-01-30

The (constrained) canonical reduction of four-dimensional self-dual Yang-Mills theory to two-dimensional Fitzhugh-Nagumo and the real Newell-Whitehead equations are considered. On the other hand, other methods and transformations are developed to obtain exact solutions for the original two-dimensional Fitzhugh-Nagumo and Newell-Whitehead equations. The corresponding gauge potential A{sub {mu}} and the gauge field strengths F{sub {mu}}{sub {nu}} are also obtained. New explicit and exact traveling wave and solitary solutions (for Fitzhugh-Nagumo and Newell-Whitehead equations) are obtained by using an improved sine-cosine method and the Wu's elimination method with the aid of Mathematica.

Exact series solution to the two flavor neutrino oscillation problem in matter

International Nuclear Information System (INIS)

Blennow, Mattias; Ohlsson, Tommy

2004-01-01

In this paper, we present a real nonlinear differential equation for the two flavor neutrino oscillation problem in matter with an arbitrary density profile. We also present an exact series solution to this nonlinear differential equation. In addition, we investigate numerically the convergence of this solution for different matter density profiles such as constant and linear profiles as well as the Preliminary Reference Earth Model describing the Earth's matter density profile. Finally, we discuss other methods used for solving the neutrino flavor evolution problem

New Exact Solutions of Time Fractional Gardner Equation by Using New Version of F -Expansion Method

International Nuclear Information System (INIS)

Pandir, Yusuf; Duzgun, Hasan Huseyin

2017-01-01

In this article, we consider analytical solutions of the time fractional derivative Gardner equation by using the new version of F-expansion method. With this proposed method multiple Jacobi elliptic functions are situated in the solution function. As a result, various exact analytical solutions consisting of single and combined Jacobi elliptic functions solutions are obtained. (paper)

Alternate Solution to Generalized Bernoulli Equations via an Integrating Factor: An Exact Differential Equation Approach

Science.gov (United States)

Tisdell, C. C.

2017-01-01

Solution methods to exact differential equations via integrating factors have a rich history dating back to Euler (1740) and the ideas enjoy applications to thermodynamics and electromagnetism. Recently, Azevedo and Valentino presented an analysis of the generalized Bernoulli equation, constructing a general solution by linearizing the problem…

An hp-adaptive strategy for the solution of the exact kernel curved wire Pocklington equation

NARCIS (Netherlands)

D.J.P. Lahaye (Domenico); P.W. Hemker (Piet)

2007-01-01

textabstractIn this paper we introduce an adaptive method for the numerical solution of the Pocklington integro-differential equation with exact kernel for the current induced in a smoothly curved thin wire antenna. The hp-adaptive technique is based on the representation of the discrete solution,

Exact solutions of linearized Schwinger endash Dyson equation of fermion self-energy

International Nuclear Information System (INIS)

Zhou, B.

1997-01-01

The Schwinger endash Dyson equation of fermion self-energy in the linearization approximation is solved exactly in a theory with gauge and effective four-fermion interactions. Different expressions for the independent solutions, which, respectively, submit to irregular and regular ultraviolet boundary condition are derived and expounded. copyright 1997 American Institute of Physics

Using quasi-guided modes for modeling the transfer behavior of bent dielectric slab waveguides

Directory of Open Access Journals (Sweden)

M. Stallein

2010-09-01

Full Text Available The connection of two straight dielectric multimode slab waveguides by a circular bent waveguide is analyzed by means of quasi-guided modes. These modes correspond to the well known leaky modes, but own real eigenvalues, thus the mathematical description is simpler. Furthermore they are derived as approximate solutions of the exact theory. This work will first give a brief introduction to the basic theory, followed by a discussion of the properties of quasi-guided modes. After a validation by comparison with a numerical simulation using the Finite Integration Technique, results for the bending loss of multimode waveguides are presented.

A two-parameter family of exact asymptotically flat solutions to the Einstein-scalar field equations

International Nuclear Information System (INIS)

Nikonov, V V; Tchemarina, Ju V; Tsirulev, A N

2008-01-01

We consider a static spherically symmetric real scalar field, minimally coupled to Einstein gravity. A two-parameter family of exact asymptotically flat solutions is obtained by using the inverse problem method. This family includes non-singular solutions, black holes and naked singularities. For each of these solutions the respective potential is partially negative but positive near spatial infinity. (comments, replies and notes)

Exact solutions of linear reaction-diffusion processes on a uniformly growing domain: criteria for successful colonization.

Science.gov (United States)

Simpson, Matthew J

2015-01-01

Many processes during embryonic development involve transport and reaction of molecules, or transport and proliferation of cells, within growing tissues. Mathematical models of such processes usually take the form of a reaction-diffusion partial differential equation (PDE) on a growing domain. Previous analyses of such models have mainly involved solving the PDEs numerically. Here, we present a framework for calculating the exact solution of a linear reaction-diffusion PDE on a growing domain. We derive an exact solution for a general class of one-dimensional linear reaction-diffusion process on 0exact solutions with numerical approximations confirms the veracity of the method. Furthermore, our examples illustrate a delicate interplay between: (i) the rate at which the domain elongates, (ii) the diffusivity associated with the spreading density profile, (iii) the reaction rate, and (iv) the initial condition. Altering the balance between these four features leads to different outcomes in terms of whether an initial profile, located near x = 0, eventually overcomes the domain growth and colonizes the entire length of the domain by reaching the boundary where x = L(t).

Exact Solution and Exotic Fluid in Cosmology

Directory of Open Access Journals (Sweden)

Phillial Oh

2012-09-01

Full Text Available We investigate cosmological consequences of nonlinear sigma model coupled with a cosmological fluid which satisfies the continuity equation. The target space action is of the de Sitter type and is composed of four scalar fields. The potential which is a function of only one of the scalar fields is also introduced. We perform a general analysis of the ensuing cosmological equations and give various critical points and their properties. Then, we show that the model exhibits an exact cosmological solution which yields a transition from matter domination into dark energy epoch and compare it with the Λ-CDM behavior. Especially, we calculate the age of the Universe and show that it is consistent with the observational value if the equation of the state ωf of the cosmological fluid is within the range of 0.13 < ωf < 0.22. Some implication of this result is also discussed.

An analytical method for solving exact solutions of the nonlinear Bogoyavlenskii equation and the nonlinear diffusive predator–prey system

Directory of Open Access Journals (Sweden)

Md. Nur Alam

2016-06-01

Full Text Available In this article, we apply the exp(-Φ(ξ-expansion method to construct many families of exact solutions of nonlinear evolution equations (NLEEs via the nonlinear diffusive predator–prey system and the Bogoyavlenskii equations. These equations can be transformed to nonlinear ordinary differential equations. As a result, some new exact solutions are obtained through the hyperbolic function, the trigonometric function, the exponential functions and the rational forms. If the parameters take specific values, then the solitary waves are derived from the traveling waves. Also, we draw 2D and 3D graphics of exact solutions for the special diffusive predator–prey system and the Bogoyavlenskii equations by the help of programming language Maple.

General exact solution for homogeneous time-dependent self-gravitating perfect fluids

International Nuclear Information System (INIS)

Gaete, P.; Hojman, R.

1988-01-01

A procedure to obtain the general exact solution of Einstein equations for a self-gravitating spherically-symmetric static perfect fluid obeying an arbitrary equation of state, is applied to time-dependent Kantowsky-Sachs line elements (with spherical, planar and hyperbolic symmetry). As in the static case, the solution is generated by an arbitrary function of the independent variable and its first derivative. To illustrate the results, the whole family of (plane-symmetric) solutions with a ''gamma-law'' equation of state is explicity obtained in terms of simple known functions. It is also shown that, while in the static plane-symmtric line elements, every metric is in one to one correspondence with a ''partner-metric'' (both originated from the same generatrix function), in this case every generatrix function univocally determines one metric. (author) [pt

A new generalized expansion method and its application in finding explicit exact solutions for a generalized variable coefficients KdV equation

International Nuclear Information System (INIS)

Sabry, R.; Zahran, M.A.; Fan Engui

2004-01-01

A generalized expansion method is proposed to uniformly construct a series of exact solutions for general variable coefficients non-linear evolution equations. The new approach admits the following types of solutions (a) polynomial solutions, (b) exponential solutions, (c) rational solutions, (d) triangular periodic wave solutions, (e) hyperbolic and solitary wave solutions and (f) Jacobi and Weierstrass doubly periodic wave solutions. The efficiency of the method has been demonstrated by applying it to a generalized variable coefficients KdV equation. Then, new and rich variety of exact explicit solutions have been found

Lie and Q-Conditional Symmetries of Reaction-Diffusion-Convection Equations with Exponential Nonlinearities and Their Application for Finding Exact Solutions

Directory of Open Access Journals (Sweden)

Roman Cherniha

2018-04-01

Full Text Available This review is devoted to search for Lie and Q-conditional (nonclassical symmetries and exact solutions of a class of reaction-diffusion-convection equations with exponential nonlinearities. A complete Lie symmetry classification of the class is derived via two different algorithms in order to show that the result depends essentially on the type of equivalence transformations used for the classification. Moreover, a complete description of Q-conditional symmetries for PDEs from the class in question is also presented. It is shown that all the well-known results for reaction-diffusion equations with exponential nonlinearities follow as particular cases from the results derived for this class of reaction-diffusion-convection equations. The symmetries obtained for constructing exact solutions of the relevant equations are successfully applied. The exact solutions are compared with those found by means of different techniques. Finally, an application of the exact solutions for solving boundary-value problems arising in population dynamics is presented.

An exact solution for quantum tunneling in a dissipative system

International Nuclear Information System (INIS)

Yu, L.H.

1996-01-01

Applying a technique developed recently for a harmonic oscillator coupled to a bath of harmonic oscillators, we present an exact solution for the tunneling problem in an Ohmic dissipative system with inverted harmonic potential. The result shows that while the dissipation tends to suppress the tunneling, the Brownian motion tends to enhance the tunneling. Whether the tunneling rate increases or not would then depend on the initial conditions. We give a specific formula to calculate the tunneling probability determined by various parameters and the initial conditions

Exact solutions and ladder operators for a new anharmonic oscillator

International Nuclear Information System (INIS)

Dong Shihai; Sun Guohua; Lozada-Cassou, M.

2005-01-01

In this Letter, we propose a new anharmonic oscillator and present the exact solutions of the Schrodinger equation with this oscillator. The ladder operators are established directly from the normalized radial wave functions and used to evaluate the closed expressions of matrix elements for some related functions. Some comments are made on the general calculation formula and recurrence relation for off-diagonal matrix elements. Finally, we show that this anharmonic oscillator possesses a hidden symmetry between E(r) and E(ir) by substituting r->ir

Renormalization of the fragmentation equation: Exact self-similar solutions and turbulent cascades

Science.gov (United States)

Saveliev, V. L.; Gorokhovski, M. A.

2012-12-01

Using an approach developed earlier for renormalization of the Boltzmann collision integral [Saveliev and Nanbu, Phys. Rev. E1539-375510.1103/PhysRevE.65.051205 65, 051205 (2002)], we derive an exact divergence form for the fragmentation operator. Then we reduce the fragmentation equation to the continuity equation in size space, with the flux given explicitly. This allows us to obtain self-similar solutions and to find the integral of motion for these solutions (we call it the bare flux). We show how these solutions can be applied as a description of cascade processes in three- and two-dimensional turbulence. We also suggested an empirical cascade model of impact fragmentation of brittle materials.

Some Exact Solutions of Boundary Layer Flows along a Vertical Plate with Buoyancy Forces Combined with Lorentz Forces under Uniform Suction

Directory of Open Access Journals (Sweden)

Asterios Pantokratoras

2008-01-01

Full Text Available Exact analytical solutions of boundary layer flows along a vertical porous plate with uniform suction are derived and presented in this paper. The solutions concern the Blasius, Sakiadis, and Blasius-Sakiadis flows with buoyancy forces combined with either MHD Lorentz or EMHD Lorentz forces. In addition, some exact solutions are presented specifically for water in the temperature range of 0∘C≤≤8∘C, where water density is nearly parabolic. Except for their use as benchmarking means for testing the numerical solution of the Navier-Stokes equations, the presented exact solutions with EMHD forces have use in flow separation control in aeronautics and hydronautics, whereas the MHD results have applications in process metallurgy and fusion technology. These analytical solutions are valid for flows with strong suction.

Polynomial conservation laws and exact solutions connected with isometrical and homothetic symmetries in the nonlinear sigma model

International Nuclear Information System (INIS)

Ivanov, G.G.

1985-01-01

In the non linear delta-model conserved tensor currents connected with the isometrical, homothetic and affine motions in the space Vsup(N) of the chiral field values are constructed. New classes of the exact solutions are obtained in the SO(3) and SO(5) invariant delta-models using the connection between the groups of isometrical and homothetic motions in the space-time and isometrical motions in Vsup(N). Some methods of obtaining exact solutions in 4-dimensional delta-model with non trivial topological charge are considered

Exact polynomial solutions of second order differential equations and their applications

International Nuclear Information System (INIS)

Zhang Yaozhong

2012-01-01

We find all polynomials Z(z) such that the differential equation where X(z), Y(z), Z(z) are polynomials of degree at most 4, 3, 2, respectively, has polynomial solutions S(z) = ∏ n i=1 (z − z i ) of degree n with distinct roots z i . We derive a set of n algebraic equations which determine these roots. We also find all polynomials Z(z) which give polynomial solutions to the differential equation when the coefficients of X(z) and Y(z) are algebraically dependent. As applications to our general results, we obtain the exact (closed-form) solutions of the Schrödinger-type differential equations describing: (1) two Coulombically repelling electrons on a sphere; (2) Schrödinger equation from the kink stability analysis of φ 6 -type field theory; (3) static perturbations for the non-extremal Reissner–Nordström solution; (4) planar Dirac electron in Coulomb and magnetic fields; and (5) O(N) invariant decatic anharmonic oscillator. (paper)

Exact mean-field theory of ionic solutions: non-Debye screening

International Nuclear Information System (INIS)

Varela, L.M.; Garcia, Manuel; Mosquera, Victor

2003-01-01

The main aim of this report is to analyze the equilibrium properties of primitive model (PM) ionic solutions in the formally exact mean-field formalism. Previously, we review the main theoretical and numerical results reported throughout the last century for homogeneous (electrolytes) and inhomogeneous (electric double layer, edl) ionic systems, starting with the classical mean-field theory of electrolytes due to Debye and Hueckel (DH). In this formalism, the effective potential is derived from the Poisson-Boltzmann (PB) equation and its asymptotic behavior analyzed in the classical Debye theory of screening. The thermodynamic properties of electrolyte solutions are briefly reviewed in the DH formalism. The main analytical and numerical extensions of DH formalism are revised, ranging from the earliest extensions that overcome the linearization of the PB equation to the more sophisticated integral equation techniques introduced after the late 1960s. Some Monte Carlo and molecular dynamic simulations are also reviewed. The potential distributions in an inhomogeneous ionic system are studied in the classical PB framework, presenting the classical Gouy-Chapman (GC) theory of the electric double layer (edl) in a brief manner. The mean-field theory is adequately contextualized using field theoretic (FT) results and it is proven that the classical PB theory is recovered at the Gaussian or one-loop level of the exact FT, and a systematic way to obtain the corrections to the DH theory is derived. Particularly, it is proven following Kholodenko and Beyerlein that corrections to DH theory effectively lead to a renormalization of charges and Debye screening length. The main analytical and numerical results for this non-Debye screening length are reviewed, ranging from asymptotic expansions, self-consistent theory, nonlinear DH results and hypernetted chain (HNC) calculations. Finally, we study the exact mean-field theory of ionic solutions, the so-called dressed-ion theory

Exact solution for MHD flow of a generalized Oldroyd-B fluid with modified Darcy's law

International Nuclear Information System (INIS)

Khan, M.; Hayat, T.; Asghar, S.

2005-12-01

This paper deals with an exact solution for the magnetohydrodynamic (MHD) flow of a generalized Oldroyd-B fluid in a circular pipe. For the description of such a fluid, the fractional calculus approach has been used throughout the analysis. Based on modified Darcy's law for generalized Oldroyd-B fluid, the velocity field is calculated analytically. Several known solutions can be recovered as the limiting cases of our solution. (author)

On exact solutions for some oscillating motions of a generalized Oldroyd-B fluid

Science.gov (United States)

Khan, M.; Anjum, Asia; Qi, Haitao; Fetecau, C.

2010-02-01

This paper deals with exact solutions for some oscillating motions of a generalized Oldroyd-B fluid. The fractional calculus approach is used in the constitutive relationship of fluid model. Analytical expressions for the velocity field and the corresponding shear stress for flows due to oscillations of an infinite flat plate as well as those induced by an oscillating pressure gradient are determined using Fourier sine and Laplace transforms. The obtained solutions are presented under integral and series forms in terms of the Mittag-Leffler functions. For α = β = 1, our solutions tend to the similar solutions for ordinary Oldroyd-B fluid. A comparison between generalized and ordinary Oldroyd-B fluids is shown by means of graphical illustrations.

Exact solution of an Ising model with competing interactions on a Cayley tree

CERN Document Server

Ganikhodjaev, N N; Wahiddin, M R B

2003-01-01

The exact solution of an Ising model with competing restricted interactions on the Cayley tree, and in the absence of an external field is presented. A critical curve is defined where it is possible to get phase transitions above it, and a single Gibbs state is obtained elsewhere.

Separation Transformation and New Exact Solutions of the (N + 1)-dimensional Dispersive Double sine-Gordon Equation

International Nuclear Information System (INIS)

Tian Ye; Chen Jing; Zhang Zhifei

2012-01-01

In this paper, the separation transformation approach is extended to the (N + 1)-dimensional dispersive double sine-Gordon equation arising in many physical systems such as the spin dynamics in the B phase of 3 He superfluid. This equation is first reduced to a set of partial differential equations and a nonlinear ordinary differential equation. Then the general solutions of the set of partial differential equations are obtained and the nonlinear ordinary differential equation is solved by F-expansion method. Finally, many new exact solutions of the (N + 1)-dimensional dispersive double sine-Gordon equation are constructed explicitly via the separation transformation. For the case of N > 2, there is an arbitrary function in the exact solutions, which may reveal more novel nonlinear structures in the high-dimensional dispersive double sine-Gordon equation.

Relativistic static thin dust disks with an inner edge: An infinite family of new exact solutions

International Nuclear Information System (INIS)

Gonzalez, Guillermo A.; Gutierrez-Pineres, Antonio C.; Vina-Cervantes, Viviana M.

2009-01-01

An infinite family of new exact solutions of the vacuum Einstein equations is presented. The solutions are static and axially symmetric and correspond to an infinite family of thin dust disks with a central inner edge. The metric functions of all the solutions can be explicitly computed, and can be expressed in a simple manner in terms of oblate spheroidal coordinates. The energy density of all the disks of the family is positive everywhere and well behaved, so that the corresponding energy-momentum tensor is in full agreement with all the energy conditions. Moreover, although the total mass of the disks is infinite, the solutions are asymptotically flat and the Riemann tensor is regular everywhere, as it is shown by computing the curvature scalars. Now, besides its importance as a new family of exact solutions of the vacuum Einstein equations, the main importance of this family of solutions is that it can be easily superposed with the Schwarzschild solution in order to describe thin disks surrounding a central black hole. Accordingly, a detailed analysis of this superposition will be presented in a subsequent paper.

On exact solutions for disturbances to the asymptotic suction boundary layer: transformation of Barnes integrals to convolution integrals

Science.gov (United States)

Russell, John

2000-11-01

A modified Orr-Sommerfeld equation that applies to the asymptotic suction boundary layer was reported by Bussmann & Münz in a wartime report dated 1942 and by Hughes & Reid in J.F.M. ( 23, 1965, p715). Fundamental systems of exact solutions of the Orr-Sommerfeld equation for this mean velocity distribution were reported by D. Grohne in an unpublished typescript dated 1950. Exact solutions of the equation of Bussmann, Münz, Hughes, & Reid were reported by P. Baldwin in Mathematika ( 17, 1970, p206). Grohne and Baldwin noticed that these exact solutions may be expressed either as Barnes integrals or as convolution integrals. In a later paper (Phil. Trans. Roy. Soc. A, 399, 1985, p321), Baldwin applied the convolution integrals in the contruction of large-Reynolds number asymptotic approximations that hold uniformly. The present talk discusses the subtleties that arise in the construction of such convolution integrals, including several not reported by Grohne or Baldwin. The aim is to recover the full set of seven solutions (one well balanced, three balanced, and three dominant-recessive) postulated by W.H. Reid in various works on the uniformly valid solutions.

Exact solutions of linear reaction-diffusion processes on a uniformly growing domain: criteria for successful colonization.

Directory of Open Access Journals (Sweden)

Matthew J Simpson

Full Text Available Many processes during embryonic development involve transport and reaction of molecules, or transport and proliferation of cells, within growing tissues. Mathematical models of such processes usually take the form of a reaction-diffusion partial differential equation (PDE on a growing domain. Previous analyses of such models have mainly involved solving the PDEs numerically. Here, we present a framework for calculating the exact solution of a linear reaction-diffusion PDE on a growing domain. We derive an exact solution for a general class of one-dimensional linear reaction-diffusion process on 0exact solutions with numerical approximations confirms the veracity of the method. Furthermore, our examples illustrate a delicate interplay between: (i the rate at which the domain elongates, (ii the diffusivity associated with the spreading density profile, (iii the reaction rate, and (iv the initial condition. Altering the balance between these four features leads to different outcomes in terms of whether an initial profile, located near x = 0, eventually overcomes the domain growth and colonizes the entire length of the domain by reaching the boundary where x = L(t.

Mechanism of the quasi-zero axial acoustic radiation force experienced by elastic and viscoelastic spheres in the field of a quasi-Gaussian beam and particle tweezing.

Science.gov (United States)

Mitri, F G; Fellah, Z E A

2014-01-01

The present analysis investigates the (axial) acoustic radiation force induced by a quasi-Gaussian beam centered on an elastic and a viscoelastic (polymer-type) sphere in a nonviscous fluid. The quasi-Gaussian beam is an exact solution of the source free Helmholtz wave equation and is characterized by an arbitrary waist w₀ and a diffraction convergence length known as the Rayleigh range z(R). Examples are found where the radiation force unexpectedly approaches closely to zero at some of the elastic sphere's resonance frequencies for kw₀≤1 (where this range is of particular interest in describing strongly focused or divergent beams), which may produce particle immobilization along the axial direction. Moreover, the (quasi)vanishing behavior of the radiation force is found to be correlated with conditions giving extinction of the backscattering by the quasi-Gaussian beam. Furthermore, the mechanism for the quasi-zero force is studied theoretically by analyzing the contributions of the kinetic, potential and momentum flux energy densities and their density functions. It is found that all the components vanish simultaneously at the selected ka values for the nulls. However, for a viscoelastic sphere, acoustic absorption degrades the quasi-zero radiation force. Copyright © 2013 Elsevier B.V. All rights reserved.

Applications of exact traveling wave solutions of Modified Liouville and the Symmetric Regularized Long Wave equations via two new techniques

Science.gov (United States)

Lu, Dianchen; Seadawy, Aly R.; Ali, Asghar

2018-06-01

In this current work, we employ novel methods to find the exact travelling wave solutions of Modified Liouville equation and the Symmetric Regularized Long Wave equation, which are called extended simple equation and exp(-Ψ(ξ))-expansion methods. By assigning the different values to the parameters, different types of the solitary wave solutions are derived from the exact traveling wave solutions, which shows the efficiency and precision of our methods. Some solutions have been represented by graphical. The obtained results have several applications in physical science.

On a revisit to the Painlevé test for integrability and exact solutions ...

Indian Academy of Sciences (India)

... the same equations and keeping the singularity manifold completely general in nature. It has been found that the equations, in real form, pass the Painlevé test for integrability. The truncation procedure of the same analysis leads to non-trivial exact solutions obtained previously and auto-Backlund transformation between ...

The exact solutions of the Schroedinger equation with the Morse potential via Laplace transforms

International Nuclear Information System (INIS)

Chen Gang

2004-01-01

In this Letter, we reduce the second-order differential equation about the one-dimensional Schroedinger equation with the Morse potential reduced to the first-order differential equation in terms of Laplace transforms and then obtain the exact bound state solutions

An exact solution of three interacting friendly walks in the bulk

International Nuclear Information System (INIS)

Tabbara, R; Owczarek, A L; Rechnitzer, A

2016-01-01

We find the exact solution of three interacting friendly directed walks on the square lattice in the bulk, modelling a system of homopolymers that can undergo a multiple polymer fusion or zipping transition by introducing two distinct interaction parameters that differentiate between the zipping of only two or all three walks. We establish functional equations for the model’s corresponding generating function that are subsequently solved exactly by means of the obstinate kernel method. We then proceed to analyse our model, first considering the case where triple-walk interaction effects are ignored, finding that our model exhibits two phases which we classify as free and gelated (or zipped) regions, with the system exhibiting a second-order phase transition. We then analyse the full model where both interaction parameters are incorporated, presenting the full phase diagram and highlighting the additional existence of a first-order gelation (zipping) boundary. (paper)

A numerical dressing method for the nonlinear superposition of solutions of the KdV equation

International Nuclear Information System (INIS)

Trogdon, Thomas; Deconinck, Bernard

2014-01-01

In this paper we present the unification of two existing numerical methods for the construction of solutions of the Korteweg–de Vries (KdV) equation. The first method is used to solve the Cauchy initial-value problem on the line for rapidly decaying initial data. The second method is used to compute finite-genus solutions of the KdV equation. The combination of these numerical methods allows for the computation of exact solutions that are asymptotically (quasi-)periodic finite-gap solutions and are a nonlinear superposition of dispersive, soliton and (quasi-)periodic solutions in the finite (x, t)-plane. Such solutions are referred to as superposition solutions. We compute these solutions accurately for all values of x and t. (paper)

New exact solutions of the Einstein—Maxwell equations for magnetostatic fields

International Nuclear Information System (INIS)

Goyal, Nisha; Gupta, R.K.

2012-01-01

The symmetry reduction method based on the Fréchet derivative of differential operators is applied to investigate symmetries of the Einstein—Maxwell field equations for magnetostatic fields, which is a coupled system of nonlinear partial differential equations of the second order. The technique yields invariant transformations that reduce the given system of partial differential equations to a system of nonlinear ordinary differential equations. Some of the reduced systems are further studied to obtain the exact solutions

A procedure to construct exact solutions of nonlinear fractional differential equations.

Science.gov (United States)

Güner, Özkan; Cevikel, Adem C

2014-01-01

We use the fractional transformation to convert the nonlinear partial fractional differential equations with the nonlinear ordinary differential equations. The Exp-function method is extended to solve fractional partial differential equations in the sense of the modified Riemann-Liouville derivative. We apply the Exp-function method to the time fractional Sharma-Tasso-Olver equation, the space fractional Burgers equation, and the time fractional fmKdV equation. As a result, we obtain some new exact solutions.

Exact solutions of the one-dimensional generalized modified complex Ginzburg-Landau equation

International Nuclear Information System (INIS)

Yomba, Emmanuel; Kofane, Timoleon Crepin

2003-01-01

The one-dimensional (1D) generalized modified complex Ginzburg-Landau (MCGL) equation for the traveling wave systems is analytically studied. Exact solutions of this equation are obtained using a method which combines the Painleve test for integrability in the formalism of Weiss-Tabor-Carnevale and Hirota technique of bilinearization. We show that pulses, fronts, periodic unbounded waves, sources, sinks and solution as collision between two fronts are the important coherent structures that organize much of the dynamical properties of these traveling wave systems. The degeneracies of the 1D generalized MCGL equation are examined as well as several of their solutions. These degeneracies include two important equations: the 1D generalized modified Schroedinger equation and the 1D generalized real modified Ginzburg-Landau equation. We obtain that the one parameter family of traveling localized source solutions called 'Nozaki-Bekki holes' become a subfamily of the dark soliton solutions in the 1D generalized modified Schroedinger limit

On the exact solutions of high order wave equations of KdV type (I)

Science.gov (United States)

Bulut, Hasan; Pandir, Yusuf; Baskonus, Haci Mehmet

2014-12-01

In this paper, by means of a proper transformation and symbolic computation, we study high order wave equations of KdV type (I). We obtained classification of exact solutions that contain soliton, rational, trigonometric and elliptic function solutions by using the extended trial equation method. As a result, the motivation of this paper is to utilize the extended trial equation method to explore new solutions of high order wave equation of KdV type (I). This method is confirmed by applying it to this kind of selected nonlinear equations.

Some exact solutions for a unidimensional fokker-planck equation by using lie symmetries

Directory of Open Access Journals (Sweden)

Hugo Hernán Ortíz-Álvarez

2015-01-01

Full Text Available The Fokker Planck equation appears in the study of diffusion phenomena, stochastics processes and quantum and classical mechanics. A particular case fromthis equation, ut − uxx − xux − u=0, is examined by the Lie group method approach. From the invariant condition it was possible to obtain the infinitesimal generators or vectors associated to this equation, identifying the corresponding symmetry groups. Exact solution were found for each one of this generators and new solution were constructed by using symmetry properties.

Breather type solutions of the vector nonlinear Schroedinger equation with quasi-constant boundary conditions

International Nuclear Information System (INIS)

Makhan'kov, V.G.; Slavov, S.I.

1989-01-01

Vector nonlinear Schroedinger equations (VS3) is investigated under quasi-constant boundary conditions. New two-soliton solutions are obtained with such non-trivial dynamics that they may be called the breather solutions. A version of the basic Novikov-Dubrovin-Krichever algebro-geometrical approach is applied to obtain breather like solutions existing for all types of internal symmetry is specified are formulated in terms of the soliton velocity expressed via the parameters of the problem. 4 refs

The exact solution to the one-dimensional Poisson–Boltzmann equation with asymmetric boundary conditions

DEFF Research Database (Denmark)

Johannessen, Kim

2014-01-01

The exact solution to the one-dimensional Poisson–Boltzmann equation with asymmetric boundary conditions can be expressed in terms of the Jacobi elliptic functions. The boundary conditions determine the modulus of the Jacobi elliptic functions. The boundary conditions can not be solved analytically...

Exact solution for the Poisson field in a semi-infinite strip.

Science.gov (United States)

Cohen, Yossi; Rothman, Daniel H

2017-04-01

The Poisson equation is associated with many physical processes. Yet exact analytic solutions for the two-dimensional Poisson field are scarce. Here we derive an analytic solution for the Poisson equation with constant forcing in a semi-infinite strip. We provide a method that can be used to solve the field in other intricate geometries. We show that the Poisson flux reveals an inverse square-root singularity at a tip of a slit, and identify a characteristic length scale in which a small perturbation, in a form of a new slit, is screened by the field. We suggest that this length scale expresses itself as a characteristic spacing between tips in real Poisson networks that grow in response to fluxes at tips.

Elliptic equation rational expansion method and new exact travelling solutions for Whitham-Broer-Kaup equations

International Nuclear Information System (INIS)

Chen Yong; Wang Qi; Li Biao

2005-01-01

Based on a new general ansatz and a general subepuation, a new general algebraic method named elliptic equation rational expansion method is devised for constructing multiple travelling wave solutions in terms of rational special function for nonlinear evolution equations (NEEs). We apply the proposed method to solve Whitham-Broer-Kaup equation and explicitly construct a series of exact solutions which include rational form solitary wave solution, rational form triangular periodic wave solutions and rational wave solutions as special cases. In addition, the links among our proposed method with the method by Fan [Chaos, Solitons and Fractals 2004;20:609], are also clarified generally

Quasi-periodic solutions of nonlinear beam equation with prescribed frequencies

International Nuclear Information System (INIS)

Chang, Jing; Gao, Yixian; Li, Yong

2015-01-01

Consider the one dimensional nonlinear beam equation u tt + u xxxx + mu + u 3 = 0 under Dirichlet boundary conditions. We show that for any m > 0 but a set of small Lebesgue measure, the above equation admits a family of small-amplitude quasi-periodic solutions with n-dimensional Diophantine frequencies. These Diophantine frequencies are the small dilation of a prescribed Diophantine vector. The proofs are based on an infinite dimensional Kolmogorov-Arnold-Moser iteration procedure and a partial Birkhoff normal form. 

Exact solitary waves of the Fisher equation

International Nuclear Information System (INIS)

Kudryashov, Nikolai A.

2005-01-01

New method is presented to search exact solutions of nonlinear differential equations. This approach is used to look for exact solutions of the Fisher equation. New exact solitary waves of the Fisher equation are given

Exact solution for the reflection and diffraction of atomic de Broglie waves by a travelling evanescent laser wave

International Nuclear Information System (INIS)

Witte, N.S.

1997-01-01

The exact solution to the problem of reflection and diffraction of atomic de Broglie waves by a travelling evanescent wave is found starting with a bare-state formulation. The solution for the wavefunctions, the tunnelling losses and the non-adiabatic losses are given exactly in terms of hyper-Bessel functions, and are valid for all detuning and Rabi frequencies, thus generalizing previous approximate methods. Furthermore we give the limiting cases of all amplitudes in the uniform semiclassical limit, which is valid in all regions including near the classical turning points, and in the large and weak coupling cases. Exact results for the zero detuning case are obtained in terms of Bessel functions. We find our uniform semiclassical limit to be closer to the exact result over the full range of parameter values than the previously reported calculations. The current knowledge of hyper-Bessel function properties is reviewed in order to apply this to the physical problems imposed

Using trees to compute approximate solutions to ordinary differential equations exactly

Science.gov (United States)

Grossman, Robert

1991-01-01

Some recent work is reviewed which relates families of trees to symbolic algorithms for the exact computation of series which approximate solutions of ordinary differential equations. It turns out that the vector space whose basis is the set of finite, rooted trees carries a natural multiplication related to the composition of differential operators, making the space of trees an algebra. This algebraic structure can be exploited to yield a variety of algorithms for manipulating vector fields and the series and algebras they generate.

Density-Dependent Conformable Space-time Fractional Diffusion-Reaction Equation and Its Exact Solutions

Science.gov (United States)

Hosseini, Kamyar; Mayeli, Peyman; Bekir, Ahmet; Guner, Ozkan

2018-01-01

In this article, a special type of fractional differential equations (FDEs) named the density-dependent conformable fractional diffusion-reaction (DDCFDR) equation is studied. Aforementioned equation has a significant role in the modelling of some phenomena arising in the applied science. The well-organized methods, including the \\exp (-φ (\\varepsilon )) -expansion and modified Kudryashov methods are exerted to generate the exact solutions of this equation such that some of the solutions are new and have been reported for the first time. Results illustrate that both methods have a great performance in handling the DDCFDR equation.

A model for studying time dependent quantum mechanical processes and its application for quasi-stationary states

International Nuclear Information System (INIS)

Revai, Janos.

1988-10-01

A model was attempted to construct which, on one hand, is flexible enough to imitate certain physical properties of real systems and, on the other hand, allows exact solution of its time dependent dynamics. This double goal is proposed to achieve by using separable interactions. A particle moving in an external field consisting of a stationary attractive and a time dependent repulsive part is proposed for the model in question. Due to the use of separable interactions, the time evolution dynamics can be solved exactly, and the model can be applied for studying time evolution of quasi-stationary states. (R.P.) 7 figs

Exact solutions to the nonlinear spinor field equations in the Goedel universe

International Nuclear Information System (INIS)

Herrera, A.

1996-01-01

The nonlinear spinor field in the external gravitational field of the Goedel universe is considered and exact static solutions to the field equations corresponding to the Lagrangians with the nonlinear terms L N =F(I S ) and L N =G(I P ) are obtained. Here F(I S ) and G(I P ) are arbitrary functions of the spinor invariants I S =S+Ψ bar Ψ and I P =P 2 =(iΨ bar γ 5 Ψ) 2 . The conditions under which one-dimensional soliton-like solutions exist are established and the role of gravity in the formation of these objects is determined. 9 refs., 1 fig

Exact solutions and numerical simulation of longitudinal vibration of the Rayleigh-Love rods with variable cross-sections

CSIR Research Space (South Africa)

Shatalov, M

2012-09-01

Full Text Available Exact solutions of equations of longitudinal vibration of conical and exponential rod are analyzed for the Rayleigh-Love model. These solutions are used as reference results for checking accuracy of the method of lines. It is shown that the method...

Exact solutions for MHD flow of couple stress fluid with heat transfer

Directory of Open Access Journals (Sweden)

Najeeb Alam Khan

2016-01-01

Full Text Available This paper aims at presenting exact solutions for MHD flow of couple stress fluid with heat transfer. The governing partial differential equations (PDEs for an incompressible MHD flow of couple stress fluid are reduced to ordinary differential equations by employing wave parameter. The methodology is implemented for linearizing the flow equations without extra transformation and restrictive assumptions. Comparison is made with the result obtained previously.

Exact travelling wave solutions of the Whitham-Broer-Kaup and Broer-Kaup-Kupershmidt equations

International Nuclear Information System (INIS)

Xu Guiqiong; Li Zhibin

2005-01-01

In this paper, an interesting fact is found that the auxiliary equation method is also applicable to a coupled system of two different equations involving both even-order and odd-order partial derivative terms. Furthermore, singular travelling wave solutions can also be obtained by considering other types of exact solutions of auxiliary equation. The Whitham-Broer-Kaup and the (2 + 1)-dimensional Broer-Kaup-Kupershmidt equations are chosen as examples to illustrate the effectiveness of the auxiliary equation method

Exact traveling wave solution of nonlinear variants of the RLW and the PHI-four equations

Energy Technology Data Exchange (ETDEWEB)

Soliman, A.A. [Department of Mathematics, Faculty of Education (AL-Arish), Suez Canal University, AL-Arish 45111 (Egypt); Department of Mathematics, Teacher' s College, Bisha, P.O. Box 551 (Saudi Arabia)], E-mail: asoliman_99@yahoo.com

2007-08-27

By means of the modified extended tanh-function (METF) method the multiple traveling wave solutions of some different kinds of nonlinear partial differential equations are presented and implemented in a computer algebraic system. The solutions for the nonlinear equations such as variants of the RLW and variant of the PHI-four equations are exactly obtained and so the efficiency of the method can be demonstrated.

Assessment of the further improved (G'/G)-expansion method and the extended tanh-method in probing exact solutions of nonlinear PDEs.

Science.gov (United States)

Akbar, M Ali; Ali, Norhashidah Hj Mohd; Mohyud-Din, Syed Tauseef

2013-01-01

The (G'/G)-expansion method is one of the most direct and effective method for obtaining exact solutions of nonlinear partial differential equations (PDEs). In the present article, we construct the exact traveling wave solutions of nonlinear evolution equations in mathematical physics via the (2 + 1)-dimensional breaking soliton equation by using two methods: namely, a further improved (G'/G)-expansion method, where G(ξ) satisfies the auxiliary ordinary differential equation (ODE) [G'(ξ)](2) = p G (2)(ξ) + q G (4)(ξ) + r G (6)(ξ); p, q and r are constants and the well known extended tanh-function method. We demonstrate, nevertheless some of the exact solutions bring out by these two methods are analogous, but they are not one and the same. It is worth mentioning that the first method has not been exercised anybody previously which gives further exact solutions than the second one. PACS numbers 02.30.Jr, 05.45.Yv, 02.30.Ik.

Lie symmetry analysis, exact solutions and conservation laws for the time fractional Caudrey-Dodd-Gibbon-Sawada-Kotera equation

Science.gov (United States)

Baleanu, Dumitru; Inc, Mustafa; Yusuf, Abdullahi; Aliyu, Aliyu Isa

2018-06-01

In this work, we investigate the Lie symmetry analysis, exact solutions and conservation laws (Cls) to the time fractional Caudrey-Dodd-Gibbon-Sawada-Kotera (CDGDK) equation with Riemann-Liouville (RL) derivative. The time fractional CDGDK is reduced to nonlinear ordinary differential equation (ODE) of fractional order. New exact traveling wave solutions for the time fractional CDGDK are obtained by fractional sub-equation method. In the reduced equation, the derivative is in Erdelyi-Kober (EK) sense. Ibragimov's nonlocal conservation method is applied to construct Cls for time fractional CDGDK.

Quasi-periodic solutions of nonlinear beam equation with prescribed frequencies

Energy Technology Data Exchange (ETDEWEB)

Chang, Jing [College of Information Technology, Jilin Agricultural University, Changchun 130118 (China); Gao, Yixian, E-mail: gaoyx643@nenu.edu.cn; Li, Yong [School of Mathematics and Statistics, and Center for Mathematics and Interdisciplinary Sciences, Northeast Normal University, Changchun 130024 (China)

2015-05-15

Consider the one dimensional nonlinear beam equation u{sub tt} + u{sub xxxx} + mu + u{sup 3} = 0 under Dirichlet boundary conditions. We show that for any m > 0 but a set of small Lebesgue measure, the above equation admits a family of small-amplitude quasi-periodic solutions with n-dimensional Diophantine frequencies. These Diophantine frequencies are the small dilation of a prescribed Diophantine vector. The proofs are based on an infinite dimensional Kolmogorov-Arnold-Moser iteration procedure and a partial Birkhoff normal form. .

Self-consistent quasi-particle RPA for the description of superfluid Fermi systems

CERN Document Server

Rahbi, A; Chanfray, G; Schuck, P

2002-01-01

Self-Consistent Quasi-Particle RPA (SCQRPA) is for the first time applied to a more level pairing case. Various filling situation and values for the coupling constant are considered. Very encouraging results in comparison with the exact solution of the model are obtaining. The nature of the low lying mode in SCQRPA is identified. The strong reduction of the number fluctuation in SCQRPA vs BCS is pointed out. The transition from superfluidity to the normal fluid case is carefully investigated.

Exact solution of thermal energy storage system using PCM flat slabs configuration

International Nuclear Information System (INIS)

Bechiri, Mohammed; Mansouri, Kacem

2013-01-01

Highlights: • An exact solution of a latent heat storage unit (LHSU) consisting of several flat slabs was obtained. • The working fluid (HTF) circulating by forced convection between the slabs charges and discharges the storage unit. • The charging/discharging process is investigated for various HTF working conditions and different design parameters. - Abstract: An analytical investigation of thermal energy storage system (TESS) consisting of several flat slabs of phase change material (PCM) is presented. The working fluid (HTF) circulating on laminar forced convection between the slabs charges and discharges the storage unit. The melting and solidification of the PCM was treated as a radial one dimensional conduction problem. The forced convective heat transfer inside the channels is analyzed by solving the energy equation, which is coupled with the heat conduction equation in the PCM container. The comparison between the present exact solution with the numerical predictions and experimental data available in literature shows good agreement. The charging/discharging process is investigated in terms of liquid–solid interface position, liquid fraction, total heat transmitted to the PCM and thermal storage efficiency for various HTF working conditions and different design parameters such as PCM slab length, fluid passage gap and thickness of PCM duct container

Exact and Heuristic Solutions to Minimize Total Waiting Time in the Blood Products Distribution Problem

Directory of Open Access Journals (Sweden)

Amir Salehipour

2012-01-01

Full Text Available This paper presents a novel application of operations research to support decision making in blood distribution management. The rapid and dynamic increasing demand, criticality of the product, storage, handling, and distribution requirements, and the different geographical locations of hospitals and medical centers have made blood distribution a complex and important problem. In this study, a real blood distribution problem containing 24 hospitals was tackled by the authors, and an exact approach was presented. The objective of the problem is to distribute blood and its products among hospitals and medical centers such that the total waiting time of those requiring the product is minimized. Following the exact solution, a hybrid heuristic algorithm is proposed. Computational experiments showed the optimal solutions could be obtained for medium size instances, while for larger instances the proposed hybrid heuristic is very competitive.

An exact solution of two friendly interacting directed walks near a sticky wall

International Nuclear Information System (INIS)

Tabbara, R; Owczarek, A L; Rechnitzer, A

2014-01-01

We find the exact solution of two interacting friendly directed walks (modelling polymers) on the square lattice. These walks are confined to the quarter plane by a horizontal attractive surface, to capture the effects of DNA-denaturation and adsorption. We find the solution to the model’s corresponding generating function by means of the obstinate kernel method. Specifically, we apply this technique in two different instances to establish partial solutions for two simplified generating functions of the same underlying model that ignore either surface or shared contacts. We then subsequently combine our two partial solutions to find the solution for the full generating function in terms of the two simpler variants. This expression guides our analysis of the model, where we find the system exhibits four phases, and proceed to delineate the full phase diagram, showing that all observed phase transitions are second-order. (paper)

An Exact Analytical Solution to Exponentially Tapered Piezoelectric Energy Harvester

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H. Salmani

2015-01-01

Full Text Available It has been proven that tapering the piezoelectric beam through its length optimizes the power extracted from vibration based energy harvesting. This phenomenon has been investigated by some researchers using semianalytical, finite element and experimental methods. In this paper, an exact analytical solution is presented to calculate the power generated from vibration of exponentially tapered unimorph and bimorph with series and parallel connections. The mass normalized mode shapes of the exponentially tapered piezoelectric beam with tip mass are implemented to transfer the proposed electromechanical coupled equations into modal coordinates. The steady states harmonic solution results are verified both numerically and experimentally. Results show that there exist values for tapering parameter and electric resistance in a way that the output power per mass of the energy harvester will be maximized. Moreover it is concluded that the electric resistance must be higher than a specified value for gaining more power by tapering the beam.

Exact Solution of a Strongly Coupled Gauge Theory in 0 +1 Dimensions

Science.gov (United States)

Krishnan, Chethan; Kumar, K. V. Pavan

2018-05-01

Gauged tensor models are a class of strongly coupled quantum mechanical theories. We present the exact analytic solution of a specific example of such a theory: namely, the smallest colored tensor model due to Gurau and Witten that exhibits nonlinearities. We find explicit analytic expressions for the eigenvalues and eigenstates, and the former agree precisely with previous numerical results on (a subset of) eigenvalues of the ungauged theory. The physics of the spectrum, despite the smallness of N , exhibits rudimentary signatures of chaos. This Letter is a summary of our main results: the technical details will appear in companion paper [C. Krishnan and K. V. Pavan Kumar, Complete solution of a gauged tensor model, arXiv:1804.10103].

Towards exact solutions of the non-linear Heisenberg-Pauli-Weyl spinor equation

International Nuclear Information System (INIS)

Mielke, E.W.

1980-03-01

In ''color geometrodynamics'' fundamental spinor fields are assumed to obey a GL(2f,C) x GL(2c,C) gauge-invariant nonlinear spinor equation of the Heisenberg-Pauli-Weyl type. Quark confinement, assimilating a scheme of Salam and Strathdee, is (partially) mediated by the tensor ''gluons'' of strong gravity. This hypothesis is incorporated into the model by considering the nonlinear Dirac equation in a curved space-time of hadronic dimensions. Disregarding internal degrees of freedom, it is then feasible, for a particular background space-time, to obtain exact solutions of the spherical bound-state problem. Finally, these solutions are tentatively interpreted as droplet-type solitons and remarks on their interrelation with Wheeler's geon construction are made. (author)

Marginalism, quasi-marginalism and critical phenomena in micellar solutions

International Nuclear Information System (INIS)

Reatto, L.

1986-01-01

The observed nonuniversal critical behaviour of some micellar solutions is interpreted in terms of quasi-marginalism, i.e. the presence of a coupling which scales with an exponent very close to the spatial dimensionality. This can give rise to a preasymptotic region with varying effective critical exponents with a final crossover to the Ising ones. The reduced crossover temperature is estimated to be below 10 -6 . The exponents β and γ measured in C 12 e 5 are in good agreement with the scaling law expected to hold for the effective exponents. The model considered by Shnidman is found unable to explain the nonuniversal critical behaviour

Lie group classification and exact solutions of the generalized Kompaneets equations

Directory of Open Access Journals (Sweden)

Oleksii Patsiuk

2015-04-01

Full Text Available We study generalized Kompaneets equations (GKEs with one functional parameter, and using the Lie-Ovsiannikov algorithm, we carried out the group classification. It is shown that the kernel algebra of the full groups of the GKEs is the one-dimensional Lie algebra. Using the direct method, we find the equivalence group. We obtain six non-equivalent (up to transformations from the equivalence group GKEs that allow wider invariance algebras than the kernel one. We find a number of exact solutions of the non-linear GKE which has the maximal symmetry properties.

Exact analytical solution of shear-induced flexural vibration of functionally graded piezoelectric beam

Energy Technology Data Exchange (ETDEWEB)

Sharma, Pankaj, E-mail: psharma@rtu.ac.in; Parashar, Sandeep Kumar, E-mail: parashar2@yahoo.com [Mechanical Engineering Department, Rajasthan Technical University, Kota (India)

2016-05-06

The priority of this paper is to obtain the exact analytical solution for free flexural vibration of FGPM beam actuated using the d{sub 15} effect. In piezoelectric actuators, the potential use of d{sub 15} effect has been of particular interest for engineering applications since shear piezoelectric coefficient d15 is much higher than the other piezoelectric coupling constants d{sub 31} and d{sub 33}. The applications of shear actuators are to induce and control the flexural vibrations of beams and plates. In this study, a modified Timoshenko beam theory is used where electric potential is assumed to vary sinusoidaly along the thickness direction. The material properties are assumed to be graded across the thickness in accordance with power law distribution. Hamilton's principle is employed to obtain the equations of motion along with the associated boundary conditions for FGPM beams. Exact analytical solution is derived thus obtained equations of motion. Results for clamped-clamped and clamped-free boundary conditions are presented. The presented result and method shell serve as benchmark for comparing the results obtained from the other approximate methods.

Almost Surely Asymptotic Stability of Exact and Numerical Solutions for Neutral Stochastic Pantograph Equations

Directory of Open Access Journals (Sweden)

Zhanhua Yu

2011-01-01

Full Text Available We study the almost surely asymptotic stability of exact solutions to neutral stochastic pantograph equations (NSPEs, and sufficient conditions are obtained. Based on these sufficient conditions, we show that the backward Euler method (BEM with variable stepsize can preserve the almost surely asymptotic stability. Numerical examples are demonstrated for illustration.

Exact solutions of nonlinear fractional differential equations by (G′/G)-expansion method

International Nuclear Information System (INIS)

Bekir Ahmet; Güner Özkan

2013-01-01

In this paper, we use the fractional complex transform and the (G′/G)-expansion method to study the nonlinear fractional differential equations and find the exact solutions. The fractional complex transform is proposed to convert a partial fractional differential equation with Jumarie's modified Riemann—Liouville derivative into its ordinary differential equation. It is shown that the considered transform and method are very efficient and powerful in solving wide classes of nonlinear fractional order equations

Entanglement dynamics following a sudden quench: An exact solution

Science.gov (United States)

Ghosh, Supriyo; Gupta, Kumar S.; Srivastava, Shashi C. L.

2017-12-01

We present an exact and fully analytical treatment of the entanglement dynamics for an isolated system of N coupled oscillators following a sudden quench of the system parameters. The system is analyzed using the solutions of the time-dependent Schrodinger's equation, which are obtained by solving the corresponding nonlinear Ermakov equations. The entanglement entropies exhibit a multi-oscillatory behaviour, where the number of dynamically generated time scales increases with N. The harmonic chains exhibit entanglement revival and for larger values of N (> 10), we find near-critical logarithmic scaling for the entanglement entropy, which is modulated by a time-dependent factor. The N = 2 case is equivalent to the two-site Bose-Hubbard model in the tunneling regime, which is amenable to empirical realization in cold-atom systems.

Noether symmetries of a modified model in teleparallel gravity and a new approach for exact solutions

Energy Technology Data Exchange (ETDEWEB)

Tajahmad, Behzad [University of Tabriz, Faculty of Physics, Tabriz (Iran, Islamic Republic of)

2017-04-15

In this paper, we present the Noether symmetries of flat FRW spacetime in the context of a new action in teleparallel gravity which we construct based on the f(R) version. This modified action contains a coupling between the scalar field potential and magnetism. Also, we introduce an innovative approach, the beyond Noether symmetry (B.N.S.) approach, for exact solutions which carry more conserved currents than the Noether approach. By data analysis of the exact solutions, obtained from the Noether approach, late-time acceleration and phase crossing are realized, and some deep connections with observational data such as the age of the universe, the present value of the scale factor as well as the state and deceleration parameters are observed. In the B.N.S. approach, we consider the dark energy dominated era. (orig.)

Noether symmetries of a modified model in teleparallel gravity and a new approach for exact solutions

International Nuclear Information System (INIS)

Tajahmad, Behzad

2017-01-01

In this paper, we present the Noether symmetries of flat FRW spacetime in the context of a new action in teleparallel gravity which we construct based on the f(R) version. This modified action contains a coupling between the scalar field potential and magnetism. Also, we introduce an innovative approach, the beyond Noether symmetry (B.N.S.) approach, for exact solutions which carry more conserved currents than the Noether approach. By data analysis of the exact solutions, obtained from the Noether approach, late-time acceleration and phase crossing are realized, and some deep connections with observational data such as the age of the universe, the present value of the scale factor as well as the state and deceleration parameters are observed. In the B.N.S. approach, we consider the dark energy dominated era. (orig.)

Mathematical modeling and exact solutions to rotating flows of a Burgers' fluid

International Nuclear Information System (INIS)

Hayat, T.

2005-12-01

The aim of this study is to provide the modeling and exact analytic solutions for hydromagnetic oscillatory rotating flows of an incompressible Burgers' fluid bounded by a plate. The governing time-dependent equation for the Burgers' fluid is different than those from the Navier-Stokes' equation. The entire system is assumed to rotate around an axis normal to the plate. The governing equations for this investigation are solved analytically for two physical problems. The solutions for the three cases, when the two times angular velocity is greater than the frequency of oscillation or it is smaller than the frequency or it is equal to the frequency (resonant case), are discussed in second problem. In Burgers' fluid, it is also found that hydromagnetic solution in the resonant case satisfies the boundary condition at infinity. Moreover, the obtained analytical results reduce to several previously published results as the special cases. (author)

Some new exact solitary wave solutions of the van der Waals model arising in nature

Science.gov (United States)

Bibi, Sadaf; Ahmed, Naveed; Khan, Umar; Mohyud-Din, Syed Tauseef

2018-06-01

This work proposes two well-known methods, namely, Exponential rational function method (ERFM) and Generalized Kudryashov method (GKM) to seek new exact solutions of the van der Waals normal form for the fluidized granular matter, linked with natural phenomena and industrial applications. New soliton solutions such as kink, periodic and solitary wave solutions are established coupled with 2D and 3D graphical patterns for clarity of physical features. Our comparison reveals that the said methods excel several existing methods. The worked-out solutions show that the suggested methods are simple and reliable as compared to many other approaches which tackle nonlinear equations stemming from applied sciences.

Greedy solution of ill-posed problems: error bounds and exact inversion

International Nuclear Information System (INIS)

Denis, L; Lorenz, D A; Trede, D

2009-01-01

The orthogonal matching pursuit (OMP) is a greedy algorithm to solve sparse approximation problems. Sufficient conditions for exact recovery are known with and without noise. In this paper we investigate the applicability of the OMP for the solution of ill-posed inverse problems in general, and in particular for two deconvolution examples from mass spectrometry and digital holography, respectively. In sparse approximation problems one often has to deal with the problem of redundancy of a dictionary, i.e. the atoms are not linearly independent. However, one expects them to be approximatively orthogonal and this is quantified by the so-called incoherence. This idea cannot be transferred to ill-posed inverse problems since here the atoms are typically far from orthogonal. The ill-posedness of the operator probably causes the correlation of two distinct atoms to become huge, i.e. that two atoms look much alike. Therefore, one needs conditions which take the structure of the problem into account and work without the concept of coherence. In this paper we develop results for the exact recovery of the support of noisy signals. In the two examples, mass spectrometry and digital holography, we show that our results lead to practically relevant estimates such that one may check a priori if the experimental setup guarantees exact deconvolution with OMP. Especially in the example from digital holography, our analysis may be regarded as a first step to calculate the resolution power of droplet holography

Homoclinic orbits around spinning black holes. I. Exact solution for the Kerr separatrix

International Nuclear Information System (INIS)

Levin, Janna; Perez-Giz, Gabe

2009-01-01

For equatorial Kerr orbits, we show that each separatrix between bound and plunging geodesics is a homoclinic orbit--an orbit that asymptotes to an energetically-bound, unstable circular orbit. We derive exact expressions for these trajectories in terms of elementary functions. We also clarify the formal connection between the separatrix and zoom-whirl orbits and show that, contrary to popular belief, zoom-whirl behavior is not intrinsically a near-separatrix phenomenon. This paper focuses on homoclinic behavior in physical space, while in a companion paper we paint the complementary phase space portrait. Although they refer to geodesic motion, the exact solutions for the Kerr separatrix could be useful for analytic or numerical studies of eccentric transitions from orbital to plunging motion under the dissipative effects of gravitational radiation.

New exact solutions of the Tzitzéica-type equations in non-linear optics using the expa function method

Science.gov (United States)

Hosseini, K.; Ayati, Z.; Ansari, R.

2018-04-01

One specific class of non-linear evolution equations, known as the Tzitzéica-type equations, has received great attention from a group of researchers involved in non-linear science. In this article, new exact solutions of the Tzitzéica-type equations arising in non-linear optics, including the Tzitzéica, Dodd-Bullough-Mikhailov and Tzitzéica-Dodd-Bullough equations, are obtained using the expa function method. The integration technique actually suggests a useful and reliable method to extract new exact solutions of a wide range of non-linear evolution equations.

Exact solution of the Klein-Gordon equation for the PT-symmetric generalized Woods-Saxon potential by the Nikiforov-Uvarov method

International Nuclear Information System (INIS)

Ikhdair, S.M.; Sever, R.

2007-01-01

The exact solution of the one-dimensional Klein-Gordon equation of the PT-symmetric generalized Woods-Saxon potential is obtained. The exact energy eigenvalues and wavefunctions are derived analytically by using the Nikiforov and Uvarov method. In addition, the positive and negative exact bound states of the s-states are also investigated for different types of complex generalized Woods-Saxon potentials. (Abstract Copyright [2007], Wiley Periodicals, Inc.)

Exact solutions of the dirac equation for an electron in magnetic field with shape invariant method

International Nuclear Information System (INIS)

Setare, M.R.; Hatami, O.

2008-01-01

Based on the shape invariance property we obtain exact solutions of the Virac equation for an electron moving in the presence of a certain varying magnetic Geld, then we also show its non-relativistic limit. (authors)

Class of Exact Solutions for a Cosmological Model of Unified Gravitational and Quintessence Fields

Science.gov (United States)

Asenjo, Felipe A.; Hojman, Sergio A.

2017-07-01

A new approach to tackle Einstein equations for an isotropic and homogeneous Friedmann-Robertson-Walker Universe in the presence of a quintessence scalar field is devised. It provides a way to get a simple exact solution to these equations. This solution determines the quintessence potential uniquely and it differs from solutions which have been used to study inflation previously. It relays on a unification of geometry and dark matter implemented through the definition of a functional relation between the scale factor of the Universe and the quintessence field. For a positive curvature Universe, this solution produces perpetual accelerated expansion rate of the Universe, while the Hubble parameter increases abruptly, attains a maximum value and decreases thereafter. The behavior of this cosmological solution is discussed and its main features are displayed. The formalism is extended to include matter and radiation.

A new analytical approach for limit cycles and quasi-periodic solutions of nonlinear oscillators: the example of the forced Van der Pol Duffing oscillator

International Nuclear Information System (INIS)

Shukla, Anant Kant; Ramamohan, T R; Srinivas, S

2014-01-01

In this paper we propose a technique to obtain limit cycles and quasi-periodic solutions of forced nonlinear oscillators. We apply this technique to the forced Van der Pol oscillator and the forced Van der Pol Duffing oscillator and obtain for the first time their limit cycles (periodic) and quasi-periodic solutions analytically. We introduce a modification of the homotopy analysis method to obtain these solutions. We minimize the square residual error to obtain accurate approximations to these solutions. The obtained analytical solutions are convergent and agree well with numerical solutions even at large times. Time trajectories of the solution, its first derivative and phase plots are presented to confirm the validity of the proposed approach. We also provide rough criteria for the determination of parameter regimes which lead to limit cycle or quasi-periodic behaviour. (papers)

The stationary sine-Gordon equation on metric graphs: Exact analytical solutions for simple topologies

Science.gov (United States)

Sabirov, K.; Rakhmanov, S.; Matrasulov, D.; Susanto, H.

2018-04-01

We consider the stationary sine-Gordon equation on metric graphs with simple topologies. Exact analytical solutions are obtained for different vertex boundary conditions. It is shown that the method can be extended for tree and other simple graph topologies. Applications of the obtained results to branched planar Josephson junctions and Josephson junctions with tricrystal boundaries are discussed.

The Exact Solution for Linear Thermoelastic Axisymmetric Deformations of Generally Laminated Circular Cylindrical Shells

Science.gov (United States)

Nemeth, Michael P.; Schultz, Marc R.

2012-01-01

A detailed exact solution is presented for laminated-composite circular cylinders with general wall construction and that undergo axisymmetric deformations. The overall solution is formulated in a general, systematic way and is based on the solution of a single fourth-order, nonhomogeneous ordinary differential equation with constant coefficients in which the radial displacement is the dependent variable. Moreover, the effects of general anisotropy are included and positive-definiteness of the strain energy is used to define uniquely the form of the basis functions spanning the solution space of the ordinary differential equation. Loading conditions are considered that include axisymmetric edge loads, surface tractions, and temperature fields. Likewise, all possible axisymmetric boundary conditions are considered. Results are presented for five examples that demonstrate a wide range of behavior for specially orthotropic and fully anisotropic cylinders.

Exact Time-Dependent Wave Functions of a Confined Time-Dependent Harmonic Oscillator with Two Moving Boundaries

International Nuclear Information System (INIS)

Lo, C.F.

2009-01-01

By applying the standard analytical techniques of solving partial differential equations, we have obtained the exact solution in terms of the Fourier sine series to the time-dependent Schroedinger equation describing a quantum one-dimensional harmonic oscillator of time-dependent frequency confined in an infinite square well with the two walls moving along some parametric trajectories. Based upon the orthonormal basis of quasi-stationary wave functions, the exact propagator of the system has also been analytically derived. Special cases like (i) a confined free particle, (ii) a confined time-independent harmonic oscillator, and (iii) an aging oscillator are examined, and the corresponding time-dependent wave functions are explicitly determined. Besides, the approach has been extended to solve the case of a confined generalized time-dependent harmonic oscillator for some parametric moving boundaries as well. (general)

Analytical and exact solutions of the spherical and cylindrical diodes of Langmuir-Blodgett law

Science.gov (United States)

Torres-Cordoba, Rafael; Martinez-Garcia, Edgar

2017-10-01

This paper discloses the exact solutions of a mathematical model that describes the cylindrical and spherical electron current emissions within the context of a physics approximation method. The solution involves analyzing the 1D nonlinear Poisson equation, for the radial component. Although an asymptotic solution has been previously obtained, we present a theoretical solution that satisfies arbitrary boundary conditions. The solution is found in its parametric form (i.e., φ(r )=φ(r (τ)) ) and is valid when the electric field at the cathode surface is non-zero. Furthermore, the non-stationary spatial solution of the electric potential between the anode and the cathode is also presented. In this work, the particle-beam interface is considered to be at the end of the plasma sheath as described by Sutherland et al. [Phys. Plasmas 12, 033103 2005]. Three regimes of space charge effects—no space charge saturation, space charge limited, and space charge saturation—are also considered.

On inclusion of the Pauli principle in the quasi particle-phonon nuclear model

International Nuclear Information System (INIS)

Soloviev, V.G.

1979-01-01

The Pauli principle in odd-even, even-odd and even-even nuclei in the quasi particle-phonon nuclear model is considered. It is shown that the Pauli principle can excactly be taken into account. The exact and approximate secular equations are obtained for the wave function containing the one-quasi particle and quasi particle plus phonon components. The effect of the Pauli principle is discussed, when the wave function contains the one- and two-phonon components. In both the cases the poles are shifted in the secular equations and the quasi particle-phonon interaction terms are added. The number of quasi particles in the ground states is estimated. It is stated that in the majority of deformed nuclei the correlations in the ground states are small. It is shown that within the quasi particle-phonon nuclear model the calculations can be performed with the exact commutation relations

Hole subbands in quantum wells: exact solution for six-dimensional Luttinger–Kohn Hamiltonian

International Nuclear Information System (INIS)

Belykh, V G; Tulupenko, V N

2009-01-01

The exact solution for wavefunctions of six-dimensional Luttinger–Kohn Hamiltonian, describing the valence band of cubic semiconductors in the effective mass approximation, is derived. The problem of space quantization for a rectangular quantum well with finite depth is solved. The wavefunctions of carriers in the quantum well are built up of a complete set of exact wavefunctions for the bulk materials constituting the heterojunction. Obtained formulae for wavefunctions permit one to derive the analytical expression for a determinant, which nulls give the allowed energy values. Comparison of the energy spectra for the Si/Si 0.88 Ge 0.12 quantum well obtained in the framework of the developed technique, and using four-dimensional Luttinger–Kohn Hamiltonian allows us to trace clearly the impact of the spin–orbit interaction on the formation of the energy spectrum for the quantum well

A Lie-admissible method of integration of Fokker-Planck equations with non-linear coefficients (exact and numerical solutions)

International Nuclear Information System (INIS)

Fronteau, J.; Combis, P.

1984-08-01

A Lagrangian method is introduced for the integration of non-linear Fokker-Planck equations. Examples of exact solutions obtained in this way are given, and also the explicit scheme used for the computation of numerical solutions. The method is, in addition, shown to be of a Lie-admissible type

Exact solution of a key equation in a finite stellar atmosphere by the method of Laplace transform and linear singular operators

International Nuclear Information System (INIS)

Das, R.N.

1980-01-01

The key equation which commonly appears for radiative transfer in a finite stellar atmosphere having ground reflection according to Lambert's law is considered in this paper. The exact solution of this equation is obtained for surface quantities in terms of the X-Y equations of Chandrasekhar by the method of Laplace transform and linear singular operators. This exact method is widely applicable for obtaining the solution for surface quantities in a finite atmosphere. (orig.)

A geometric method of constructing exact solutions in modified f(R,T)-gravity with Yang-Mills and Higgs interactions

CERN Document Server

Vacaru, Sergiu I.; Yazici, Enis

2014-01-01

We show that a geometric techniques can be elaborated and applied for constructing generic off-diagonal exact solutions in $f(R,T)$--modified gravity for systems of gravitational-Yang-Mills-Higgs equations. The corresponding classes of metrics and generalized connections are determined by generating and integration functions which depend, in general, on all space and time coordinates and may possess, or not, Killing symmetries. For nonholonomic constraints resulting in Levi-Civita configurations, we can extract solutions of the Einstein-Yang-Mills-Higgs equations. We show that the constructions simplify substantially for metrics with at least one Killing vector. There are provided and analyzed some examples of exact solutions describing generic off-diagonal modifications to black hole/ellipsoid and solitonic configurations.

New exact solutions to MKDV-Burgers equation and (2 + 1)-dimensional dispersive long wave equation via extended Riccati equation method

International Nuclear Information System (INIS)

Kong Cuicui; Wang Dan; Song Lina; Zhang Hongqing

2009-01-01

In this paper, with the aid of symbolic computation and a general ansaetz, we presented a new extended rational expansion method to construct new rational formal exact solutions to nonlinear partial differential equations. In order to illustrate the effectiveness of this method, we apply it to the MKDV-Burgers equation and the (2 + 1)-dimensional dispersive long wave equation, then several new kinds of exact solutions are successfully obtained by using the new ansaetz. The method can also be applied to other nonlinear partial differential equations.

Numerical Uncertainty Analysis for Computational Fluid Dynamics using Student T Distribution -- Application of CFD Uncertainty Analysis Compared to Exact Analytical Solution

Science.gov (United States)

Groves, Curtis E.; Ilie, marcel; Shallhorn, Paul A.

2014-01-01

Computational Fluid Dynamics (CFD) is the standard numerical tool used by Fluid Dynamists to estimate solutions to many problems in academia, government, and industry. CFD is known to have errors and uncertainties and there is no universally adopted method to estimate such quantities. This paper describes an approach to estimate CFD uncertainties strictly numerically using inputs and the Student-T distribution. The approach is compared to an exact analytical solution of fully developed, laminar flow between infinite, stationary plates. It is shown that treating all CFD input parameters as oscillatory uncertainty terms coupled with the Student-T distribution can encompass the exact solution.

Mathematical and physical aspects of controlling the exact solutions of the 3D Gross-Pitaevskii equation

International Nuclear Information System (INIS)

Fedele, Renato; Jovanovic, Dusan; De Nicola, Sergio; Eliasson, Bengt; Shukla, Padma K.

2010-01-01

The possibility of the decomposition of the three-dimensional (3D) Gross-Pitaevskii equation (GPE) into a pair of coupled Schroedinger-type equations, is investigated. It is shown that, under suitable mathematical conditions, it is possible to construct the exact controlled solutions of the 3D GPE from the solutions of a linear 2D Schroedinger equation coupled with a 1D nonlinear Schroedinger equation (the transverse and longitudinal components of the GPE, respectively). The coupling between these two equations is the functional of the transverse and the longitudinal profiles. The applied method of nonlinear decomposition, called the controlling potential method (CPM), yields the full 3D solution in the form of the product of the solutions of the transverse and longitudinal components of the GPE. It is shown that the CPM constitutes a variational principle and sets up a condition on the controlling potential well. Its physical interpretation is given in terms of the minimization of the (energy) effects introduced by the control. The method is applied to the case of a parabolic external potential to construct analytically an exact BEC state in the form of a bright soliton, for which the quantitative comparison between the external and controlling potentials is presented.

A new method of solution for one-dimensional quasi-neutral bounded plasmas

Science.gov (United States)

Kamran, M.; Kuhn, S.

2010-08-01

A new method is proposed for calculating the potential distribution Φ(z) in a one-dimensional quasi-neutral bounded plasma; Φ(z) is assumed to satisfy a quasi-neutrality condition (plasma equation) of the form ni{Φ(z)} = ne(Φ), where the electron density ne is a given function of Φ and the ion density ni is expressed in terms of trajectory integrals of the ion kinetic equation. While previous methods relied on formally solving a global integral equation (Riemann, Phys. Plasmas, vol. 13, 2006, paper no. 013503; Kos et al., Phys. Plasmas, vol. 16, 2009, paper no. 093503), the present method is characterized by piecewise analytic solution of the plasma equation in reasonably small intervals of z. As a first concrete application, Φ(z) is found analytically through order z4 near the center of a collisionless Tonks-Langmuir discharge with a cold-ion source.

Exact solution of the O(n) model on a random lattice

DEFF Research Database (Denmark)

Eynard, B.; Kristjansen, C.

1995-01-01

We present an exact solution of the O(n) model on a random lattice. The coupling constant space of our model is parametrized in terms of a set of moment variables and the same type of universality with respect to the potential as observed for the one-matrix model is found. In addition we find...... a large degree of universality with respect to n; namely for n gE ] - 2,2[ the solution can be presented in a form which is valid not only for any potential, but also for any n (not necessarily rational). The cases n = ±2 are treated separately. We give explicit expressions for the genus-zero contribution...... to the one- and two-loop correlators as well as for the genus-one contribution to the one-loop correlator and the free energy. It is shown how one can obtain from these results any multi-loop correlator and the free energy to any genus and the structure of the higher-genera contributions is described...

EXACT SOLUTION OF HEAT CONDUCTION IN A TWO-DOMAIN COMPOSITE CYLINDER WITH AN ORTHOTROPIC OUTER LAYER

International Nuclear Information System (INIS)

AVILES-RAMOS, C.; RUDY, C.

2000-01-01

The transient exact solution of heat conduction in a two-domain composite cylinder is developed using the separation of variables technique. The inner cylinder is isotropic and the outer cylindrical layer is orthotropic. Temperature solutions are obtained for boundary conditions of the first and second kinds at the outer surface of the orthotropic layer. These solutions are applied to heat flow calorimeters modeling assuming that there is heat generation due to nuclear reactions in the inner cylinder. Heat flow calorimeter simulations are carried out assuming that the inner cylinder is filled with plutonium oxide powder. The first objective in these simulations is to predict the onset of thermal equilibrium of the calorimeter with its environment. Two types of boundary conditions at the outer surface of the orthotropic layer are used to predict thermal equilibrium. The procedure developed to carry out these simulations can be used as a guideline for the design of calorimeters. Another important application of these solutions is on the estimation of thermophysical properties of orthotropic cylinders. The thermal conductivities in the vertical, radial and circumferential directions of the orthotropic outer layer can be estimated using this exact solution and experimental data. Simultaneous estimation of the volumetric heat capacity and thermal conductivities is also possible. Furthermore, this solution has potential applications to the solution of the inverse heat conduction problem in this cylindrical geometry. An interesting feature of the construction of this solution is that two different sets of eigenfunctions need to be considered in the eigenfunction expansion. These eigenfunctions sets depend on the relative values of the thermal diffusivity of the inner cylinder and the thermal diffusivity in the vertical direction of the outer cylindrical layer

The general Klein-Gordon-Schroedinger system: modulational instability and exact solutions

International Nuclear Information System (INIS)

Tang Xiaoyan; Ding Wei

2008-01-01

The general Klein-Gordon-Schroedinger (gKGS) system is studied where the cubic auto-interactions are introduced in both the nonlinear Schroedinger and the nonlinear Klein-Gordon fields. We first investigate the modulational instability (MI) of the system, and thus derive the general dispersion relation between the frequency and wavenumber of the modulating perturbations, which demonstrates many possibilities for the MI regions. Using the travelling wave reduction, the gKGS system is greatly simplified. Via a simple function expansion method, we obtain some exact travelling wave solutions. Under some special parameter values, some representative wave structures are graphically displayed including the kink, anti-kink, bright, dark, grey and periodic solitons

Exact solution to the 'auxiliary extra-dimension' model of massive gravity

International Nuclear Information System (INIS)

Hassan, S.F.; Rosen, Rachel A.

2011-01-01

The 'auxiliary extra-dimension' model was proposed in order to provide a geometrical interpretation to modifications of general relativity, in particular to non-linear massive gravity. In this context, the theory was shown to be ghost free to third order in perturbations, in the decoupling limit. In this work, we exactly solve the equation of motion in the extra dimension, to obtain a purely 4-dimensional theory. Using this solution, it is shown that the ghost appears at the fourth order and beyond. We explore potential modifications to address the ghost issue and find that their consistent implementation requires going beyond the present framework.

Exact and Numerical Solutions of a Spatially-Distributed Mathematical Model for Fluid and Solute Transport in Peritoneal Dialysis

Directory of Open Access Journals (Sweden)

Roman Cherniha

2016-06-01

Full Text Available The nonlinear mathematical model for solute and fluid transport induced by the osmotic pressure of glucose and albumin with the dependence of several parameters on the hydrostatic pressure is described. In particular, the fractional space available for macromolecules (albumin was used as a typical example and fractional fluid void volume were assumed to be different functions of hydrostatic pressure. In order to find non-uniform steady-state solutions analytically, some mathematical restrictions on the model parameters were applied. Exact formulae (involving hypergeometric functions for the density of fluid flux from blood to tissue and the fluid flux across tissues were constructed. In order to justify the applicability of the analytical results obtained, a wide range of numerical simulations were performed. It was found that the analytical formulae can describe with good approximation the fluid and solute transport (especially the rate of ultrafiltration for a wide range of values of the model parameters.

Exact solutions of the Dirac equation with a Coulomb plus scalar potential in 2 + 1 dimensions

International Nuclear Information System (INIS)

Dong, Shihai; Gu, Xiaoyan; Ma, Zhongqi; Dong, Shishan

2002-01-01

The exact solutions of the (2+1)-dimensional Dirac equation with a Coulomb potential and a scalar one are analytically presented by studying the second-order differential equations obtained from a pair of coupled first-order ones. The eigenvalues are studied in some detail. (author)

Exact solutions with solitary patterns for the Zakharov-Kuznetsov equations with fully nonlinear dispersion

International Nuclear Information System (INIS)

Inc, Mustafa

2007-01-01

In this paper, the nonlinear dispersive Zakharov-Kuznetsov ZK(m, n, k) equations are solved exactly by using the Adomian decomposition method. The two special cases, ZK(2, 2, 2) and ZK(3, 3, 3), are chosen to illustrate the concrete scheme of the decomposition method in ZK(m, n, k) equations. General formulas for the solutions of ZK(m, n, k) equations are established

Exact solution for the quench dynamics of a nested integrable system

Science.gov (United States)

Mestyán, Márton; Bertini, Bruno; Piroli, Lorenzo; Calabrese, Pasquale

2017-08-01

Integrable models provide an exact description for a wide variety of physical phenomena. For example nested integrable systems contain different species of interacting particles with a rich phenomenology in their collective behavior, which is the origin of the unconventional phenomenon of spin-charge separation. So far, however, most of the theoretical work in the study of non-equilibrium dynamics of integrable systems has focussed on models with an elementary (i.e. not nested) Bethe ansatz. In this work we explicitly investigate quantum quenches in nested integrable systems, by generalizing the application of the quench action approach. Specifically, we consider the spin-1 Lai-Sutherland model, described, in the thermodynamic limit, by the theory of two different species of Bethe-ansatz particles, each one forming an infinite number of bound states. We focus on the situation where the quench dynamics starts from a simple matrix product state for which the overlaps with the eigenstates of the Hamiltonian are known. We fully characterize the post-quench steady state and perform several consistency checks for the validity of our results. Finally, we provide predictions for the propagation of entanglement and mutual information after the quench, which can be used as signature of the quasi-particle content of the model.

Exact discretization of Schrödinger equation

Energy Technology Data Exchange (ETDEWEB)

Tarasov, Vasily E., E-mail: tarasov@theory.sinp.msu.ru

2016-01-08

There are different approaches to discretization of the Schrödinger equation with some approximations. In this paper we derive a discrete equation that can be considered as exact discretization of the continuous Schrödinger equation. The proposed discrete equation is an equation with difference of integer order that is represented by infinite series. We suggest differences, which are characterized by power-law Fourier transforms. These differences can be considered as exact discrete analogs of derivatives of integer orders. Physically the suggested discrete equation describes a chain (or lattice) model with long-range interaction of power-law form. Mathematically it is a uniquely highlighted difference equation that exactly corresponds to the continuous Schrödinger equation. Using the Young's inequality for convolution, we prove that suggested differences are operators on the Hilbert space of square-summable sequences. We prove that the wave functions, which are exact discrete analogs of the free particle and harmonic oscillator solutions of the continuous Schrödinger equations, are solutions of the suggested discrete Schrödinger equations. - Highlights: • Exact discretization of the continuous Schrödinger equation is suggested. • New long-range interactions of power-law form are suggested. • Solutions of discrete Schrödinger equation are exact discrete analogs of continuous solutions.

Exact discretization of Schrödinger equation

International Nuclear Information System (INIS)

Tarasov, Vasily E.

2016-01-01

There are different approaches to discretization of the Schrödinger equation with some approximations. In this paper we derive a discrete equation that can be considered as exact discretization of the continuous Schrödinger equation. The proposed discrete equation is an equation with difference of integer order that is represented by infinite series. We suggest differences, which are characterized by power-law Fourier transforms. These differences can be considered as exact discrete analogs of derivatives of integer orders. Physically the suggested discrete equation describes a chain (or lattice) model with long-range interaction of power-law form. Mathematically it is a uniquely highlighted difference equation that exactly corresponds to the continuous Schrödinger equation. Using the Young's inequality for convolution, we prove that suggested differences are operators on the Hilbert space of square-summable sequences. We prove that the wave functions, which are exact discrete analogs of the free particle and harmonic oscillator solutions of the continuous Schrödinger equations, are solutions of the suggested discrete Schrödinger equations. - Highlights: • Exact discretization of the continuous Schrödinger equation is suggested. • New long-range interactions of power-law form are suggested. • Solutions of discrete Schrödinger equation are exact discrete analogs of continuous solutions.

Lie symmetry analysis, conservation laws and exact solutions of the seventh-order time fractional Sawada–Kotera–Ito equation

Directory of Open Access Journals (Sweden)

Emrullah Yaşar

Full Text Available In this paper Lie symmetry analysis of the seventh-order time fractional Sawada–Kotera–Ito (FSKI equation with Riemann–Liouville derivative is performed. Using the Lie point symmetries of FSKI equation, it is shown that it can be transformed into a nonlinear ordinary differential equation of fractional order with a new dependent variable. In the reduced equation the derivative is in Erdelyi–Kober sense. Furthermore, adapting the Ibragimov’s nonlocal conservation method to time fractional partial differential equations, we obtain conservation laws of the underlying equation. In addition, we construct some exact travelling wave solutions for the FSKI equation using the sub-equation method. Keywords: Fractional Sawada–Kotera–Ito equation, Lie symmetry, Riemann–Liouville fractional derivative, Conservation laws, Exact solutions

Exact solution of a coupled spin–electron linear chain composed of localized Ising spins and mobile electrons

International Nuclear Information System (INIS)

Čisárová, Jana; Strečka, Jozef

2014-01-01

Exact solution of a coupled spin–electron linear chain composed of localized Ising spins and mobile electrons is found. The investigated spin–electron model is exactly solvable by the use of a transfer-matrix method after tracing out the degrees of freedom of mobile electrons delocalized over a couple of interstitial (decorating) sites. The exact ground-state phase diagram reveals an existence of five phases with different number of mobile electrons per unit cell, two of which are ferromagnetic, two are paramagnetic and one is antiferromagnetic. We have studied in particular the dependencies of compressibility and specific heat on temperature and electron density. - Highlights: • A coupled spin–electron chain composed of Ising spins and mobile electrons is exactly solved. • Quantum paramagnetic, ferromagnetic and antiferromagnetic ground states are found. • A compressibility shows a non-monotonous dependence on temperature and electron density. • Thermal dependences of specific heat display two distinct peaks

Modification of the Kolmogorov-Johnson-Mehl-Avrami rate equation for non-isothermal experiments and its analytical solution

OpenAIRE

Farjas, Jordi; Roura, Pere

2008-01-01

Avrami's model describes the kinetics of phase transformation under the assumption of spatially random nucleation. In this paper we provide a quasi-exact analytical solution of Avrami's model when the transformation takes place under continuous heating. This solution has been obtained with different activation energies for both nucleation and growth rates. The relation obtained is also a solution of the so-called Kolmogorov-Johnson-Mehl-Avrami transformation rate equation. The corresponding n...

Exact solutions and transformation properties of nonlinear partial differential equations from general relativity

International Nuclear Information System (INIS)

Fischer, E.

1977-01-01

Various families of exact solutions to the Einstein and Einstein--Maxwell field equations of general relativity are treated for situations of sufficient symmetry that only two independent variables arise. The mathematical problem then reduces to consideration of sets of two coupled nonlinear differential equations. The physical situations in which such equations arise include: the external gravitational field of an axisymmetric, uncharged steadily rotating body, cylindrical gravitational waves with two degrees of freedom, colliding plane gravitational waves, the external gravitational and electromagnetic fields of a static, charged axisymmetric body, and colliding plane electromagnetic and gravitational waves. Through the introduction of suitable potentials and coordinate transformations, a formalism is presented which treats all these problems simultaneously. These transformations and potentials may be used to generate new solutions to the Einstein--Maxwell equations from solutions to the vacuum Einstein equations, and vice-versa. The calculus of differential forms is used as a tool for generation of similarity solutions and generalized similarity solutions. It is further used to find the invariance group of the equations; this in turn leads to various finite transformations that give new, physically distinct solutions from old. Some of the above results are then generalized to the case of three independent variables

Exact solutions to plaquette Ising models with free and periodic boundaries

International Nuclear Information System (INIS)

Mueller, Marco; Johnston, Desmond A.; Janke, Wolfhard

2017-01-01

An anisotropic limit of the 3d plaquette Ising model, in which the plaquette couplings in one direction were set to zero, was solved for free boundary conditions by Suzuki (1972) , who later dubbed it the fuki-nuke, or “no-ceiling”, model. Defining new spin variables as the product of nearest-neighbour spins transforms the Hamiltonian into that of a stack of (standard) 2d Ising models and reveals the planar nature of the magnetic order, which is also present in the fully isotropic 3d plaquette model. More recently, the solution of the fuki-nuke model was discussed for periodic boundary conditions, which require a different approach to defining the product spin transformation, by Castelnovo et al. (2010) . We clarify the exact relation between partition functions with free and periodic boundary conditions expressed in terms of original and product spin variables for the 2d plaquette and 3d fuki-nuke models, noting that the differences are already present in the 1d Ising model. In addition, we solve the 2d plaquette Ising model with helical boundary conditions. The various exactly solved examples illustrate how correlations can be induced in finite systems as a consequence of the choice of boundary conditions.

New exact wave solutions for Hirota equation

Indian Academy of Sciences (India)

2Department of Engineering Sciences, Faculty of Technology and Engineering,. University ... of nonlinear partial differential equations (NPDEs) in mathematical physics. Keywords. ... This method has been successfully applied to obtain exact.

Exact ground and excited states of an antiferromagnetic quantum spin model

International Nuclear Information System (INIS)

Bose, I.

1989-08-01

A quasi-one-dimensional spin model which consists of a chain of octahedra of spins has been suggested for which a certain parameter regime of the Hamiltonian, the ground state, can be written down exactly. The ground state is highly degenerate and can be other than a singlet. Also, several excited states can be constructed exactly. The ground state is a local RVB state for which resonance is confined to rings of spins. Some exact numerical results for an octahedron of spins have also been reported. (author). 16 refs, 2 figs, 1 tab

Exact Solution of Fractional Diffusion Model with Source Term used in Study of Concentration of Fission Product in Uranium Dioxide Particle

International Nuclear Information System (INIS)

Fang Chao; Cao Jianzhu; Sun Lifeng

2011-01-01

The exact solution of fractional diffusion model with a location-independent source term used in the study of the concentration of fission product in spherical uranium dioxide (UO 2 ) particle is built. The adsorption effect of the fission product on the surface of the UO 2 particle and the delayed decay effect are also considered. The solution is given in terms of Mittag-Leffler function with finite Hankel integral transformation and Laplace transformation. At last, the reduced forms of the solution under some special physical conditions, which is used in nuclear engineering, are obtained and corresponding remarks are given to provide significant exact results to the concentration analysis of nuclear fission products in nuclear reactor. (nuclear physics)

Archimedean-type force in a cosmic dark fluid. I. Exact solutions for the late-time accelerated expansion

International Nuclear Information System (INIS)

Balakin, Alexander B.; Bochkarev, Vladimir V.

2011-01-01

We establish a new self-consistent model in order to explain from a unified viewpoint two key features of the cosmological evolution: the inflation in the early Universe and the late-time accelerated expansion. The key element of this new model is the Archimedean-type coupling of the dark matter with dark energy, which form the so-called cosmic dark fluid. We suppose that dark matter particles immersed into the dark energy reservoir are affected by the force proportional to the four-gradient of the dark energy pressure. The Archimedean-type coupling is shown to play a role of effective energy-momentum redistributor between the dark matter and the dark energy components of the dark fluid, thus providing the Universe evolution to be a quasiperiodic and/or multistage process. In the first part of the work we discuss a theoretical base and new exact solutions of the model master equations. Special attention is focused on the exact solutions, for which the scale factor is presented by the anti-Gaussian function: these solutions describe the late-time acceleration and are characterized by a nonsingular behavior in the early Universe. The second part contains qualitative and numerical analysis of the master equations; we focus there on the solutions describing a multi-inflationary Universe.

Exact analytical solution of time-independent neutron transport equation, and its applications to systems with a point source

International Nuclear Information System (INIS)

Mikata, Y.

2014-01-01

Highlights: • An exact solution for the one-speed neutron transport equation is obtained. • This solution as well as its derivation are believed to be new. • Neutron flux for a purely absorbing material with a point neutron source off the origin is obtained. • Spherically as well as cylindrically piecewise constant cross sections are studied. • Neutron flux expressions for a point neutron source off the origin are believed to be new. - Abstract: An exact analytical solution of the time-independent monoenergetic neutron transport equation is obtained in this paper. The solution is applied to systems with a point source. Systematic analysis of the solution of the time-independent neutron transport equation, and its applications represent the primary goal of this paper. To the best of the author’s knowledge, certain key results on the scalar neutron flux as well as their derivations are new. As an application of these results, a scalar neutron flux for a purely absorbing medium with a spherically piecewise constant cross section and an isotropic point neutron source off the origin as well as that for a cylindrically piecewise constant cross section with a point neutron source off the origin are obtained. Both of these results are believed to be new

Investigation of ALEGRA shock hydrocode algorithms using an exact free surface jet flow solution.

Energy Technology Data Exchange (ETDEWEB)

Hanks, Bradley Wright.; Robinson, Allen C

2014-01-01

Computational testing of the arbitrary Lagrangian-Eulerian shock physics code, ALEGRA, is presented using an exact solution that is very similar to a shaped charge jet flow. The solution is a steady, isentropic, subsonic free surface flow with significant compression and release and is provided as a steady state initial condition. There should be no shocks and no entropy production throughout the problem. The purpose of this test problem is to present a detailed and challenging computation in order to provide evidence for algorithmic strengths and weaknesses in ALEGRA which should be examined further. The results of this work are intended to be used to guide future algorithmic improvements in the spirit of test-driven development processes.

Parametric Level Statistics in Random Matrix Theory: Exact Solution

International Nuclear Information System (INIS)

Kanzieper, E.

1999-01-01

During recent several years, the theory of non-Gaussian random matrix ensembles has experienced a sound progress motivated by new ideas in quantum chromodynamics (QCD) and mesoscopic physics. Invariant non-Gaussian random matrix models appear to describe universal features of low-energy part of the spectrum of Dirac operator in QCD, and electron level statistics in normal conducting-superconducting hybrid structures. They also serve as a basis for constructing the toy models of universal spectral statistics expected at the edge of the metal-insulator transition. While conventional spectral statistics has received a detailed study in the context of RMT, quite a bit is known about parametric level statistics in non-Gaussian random matrix models. In this communication we report about exact solution to the problem of parametric level statistics in unitary invariant, U(N), non-Gaussian ensembles of N x N Hermitian random matrices with either soft or strong level confinement. The solution is formulated within the framework of the orthogonal polynomial technique and is shown to depend on both the unfolded two-point scalar kernel and the level confinement through a double integral transformation which, in turn, provides a constructive tool for description of parametric level correlations in non-Gaussian RMT. In the case of soft level confinement, the formalism developed is potentially applicable to a study of parametric level statistics in an important class of random matrix models with finite level compressibility expected to describe a disorder-induced metal-insulator transition. In random matrix ensembles with strong level confinement, the solution presented takes a particular simple form in the thermodynamic limit: In this case, a new intriguing connection relation between the parametric level statistics and the scalar two-point kernel of an unperturbed ensemble is demonstrated to emerge. Extension of the results obtained to higher-order parametric level statistics is

Generalized Bilinear Differential Operators, Binary Bell Polynomials, and Exact Periodic Wave Solution of Boiti-Leon-Manna-Pempinelli Equation

Directory of Open Access Journals (Sweden)

Huanhe Dong

2014-01-01

Full Text Available We introduce how to obtain the bilinear form and the exact periodic wave solutions of a class of (2+1-dimensional nonlinear integrable differential equations directly and quickly with the help of the generalized Dp-operators, binary Bell polynomials, and a general Riemann theta function in terms of the Hirota method. As applications, we solve the periodic wave solution of BLMP equation and it can be reduced to soliton solution via asymptotic analysis when the value of p is 5.

Exact solitary waves of the Korteveg - de Vries - Burgers equation

OpenAIRE

Kudryashov, N. A.

2004-01-01

New approach is presented to search exact solutions of nonlinear differential equations. This method is used to look for exact solutions of the Korteveg -- de Vries -- Burgers equation. New exact solitary waves of the Korteveg -- de Vries -- Burgers equation are found.

Exact solutions of the Schrödinger equation with double ring-shaped oscillator

Energy Technology Data Exchange (ETDEWEB)

Chen, Chang-Yuan, E-mail: yctcccy@163.net [School of Physics and Electronics, Yancheng Teachers University, Yancheng 224051 (China); You, Yuan; Wang, Xiao-Hua [School of Physics and Electronics, Yancheng Teachers University, Yancheng 224051 (China); Dong, Shi-Hai, E-mail: dongsh2@yahoo.com [Departamento de Física, Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Edificio 9, Unidad Profesional Adolfo López Mateos, Mexico D.F. 07738 (Mexico)

2013-09-16

We present the exact solutions of the Schrödinger equation with the double ring-shaped oscillator (DRSO) potential. By introducing a new variable x=cosθ and constructing super-universal associated Legendre polynomials we express the polar angular wave functions explicitly. We observe that the present DRSO has caused the symmetry breaking from the original spherical oscillator SU(3)⊃SO(3)⊃O(2) symmetries to the present O(2) symmetry due to the surrounded two ring-shaped inversed square potentials. Some special cases are also discussed.

Exact solutions of the Schrödinger equation with double ring-shaped oscillator

International Nuclear Information System (INIS)

Chen, Chang-Yuan; You, Yuan; Wang, Xiao-Hua; Dong, Shi-Hai

2013-01-01

We present the exact solutions of the Schrödinger equation with the double ring-shaped oscillator (DRSO) potential. By introducing a new variable x=cosθ and constructing super-universal associated Legendre polynomials we express the polar angular wave functions explicitly. We observe that the present DRSO has caused the symmetry breaking from the original spherical oscillator SU(3)⊃SO(3)⊃O(2) symmetries to the present O(2) symmetry due to the surrounded two ring-shaped inversed square potentials. Some special cases are also discussed.

Exact soliton solutions of the generalized Gross-Pitaevskii equation based on expansion method

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Ying Wang

2014-06-01

Full Text Available We give a more generalized treatment of the 1D generalized Gross-Pitaevskii equation (GGPE with variable term coefficients. External harmonic trapping potential is fully considered and the nonlinear interaction term is of arbitrary polytropic index of superfluid wave function. We also eliminate the interdependence between variable coefficients of the equation terms avoiding the restrictions that occur in some other works. The exact soliton solutions of the GGPE are obtained through the delicate combined utilization of modified lens-type transformation and F-expansion method with dominant features like soliton type properties highlighted.

Exact solutions to the Boltzmann equation by mapping the scattering integral into a differential operator

International Nuclear Information System (INIS)

Zabadal, Jorge; Borges, Volnei; Van der Laan, Flavio T.; Santos, Marcio G.

2015-01-01

This work presents a new analytical method for solving the Boltzmann equation. In this formulation, a linear differential operator is applied over the Boltzmann model, in order to produce a partial differential equation in which the scattering term is absent. This auxiliary equation is solved via reduction of order. The exact solution obtained is employed to define a precursor for the buildup factor. (author)

Exact solutions to the Boltzmann equation by mapping the scattering integral into a differential operator

Energy Technology Data Exchange (ETDEWEB)

Zabadal, Jorge; Borges, Volnei; Van der Laan, Flavio T., E-mail: jorge.zabadal@ufrgs.br, E-mail: borges@ufrgs.br, E-mail: ftvdl@ufrgs.br [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Departamento de Engenharia Mecanica. Grupo de Pesquisas Radiologicas; Ribeiro, Vinicius G., E-mail: vinicius_ribeiro@uniritter.edu.br [Centro Universitario Ritter dos Reis (UNIRITTER), Porto Alegre, RS (Brazil); Santos, Marcio G., E-mail: phd.marcio@gmail.com [Universidade Federal do Rio Grande do Sul (UFRGS), Tramandai, RS (Brazil). Departamento Interdisciplinar do Campus Litoral Norte

2015-07-01

This work presents a new analytical method for solving the Boltzmann equation. In this formulation, a linear differential operator is applied over the Boltzmann model, in order to produce a partial differential equation in which the scattering term is absent. This auxiliary equation is solved via reduction of order. The exact solution obtained is employed to define a precursor for the buildup factor. (author)

Generalized bi-quasi-variational inequalities for quasi-semi-monotone and bi-quasi-semi-monotone operators with applications in non-compact settings and minimization problems

Directory of Open Access Journals (Sweden)

Chowdhury Molhammad SR

2000-01-01

Full Text Available Results are obtained on existence theorems of generalized bi-quasi-variational inequalities for quasi-semi-monotone and bi-quasi-semi-monotone operators in both compact and non-compact settings. We shall use the concept of escaping sequences introduced by Border (Fixed Point Theorem with Applications to Economics and Game Theory, Cambridge University Press, Cambridge, 1985 to obtain results in non-compact settings. Existence theorems on non-compact generalized bi-complementarity problems for quasi-semi-monotone and bi-quasi-semi-monotone operators are also obtained. Moreover, as applications of some results of this paper on generalized bi-quasi-variational inequalities, we shall obtain existence of solutions for some kind of minimization problems with quasi- semi-monotone and bi-quasi-semi-monotone operators.

Quasi-effective medium theory for multi-layered magneto-dielectric structures

International Nuclear Information System (INIS)

Genov, Dentcho A; Mundru, Pattabhiraju C

2014-01-01

We present a quasi-effective medium theory that determines the optical properties of multi-layered composites beyond the quasi-static limit. The proposed theory exactly reproduces the far field scattering/extinction cross sections through an iterative process in which mode-dependent quasi-effective impedances of the composite system are introduced. In the large wavelength limit our theory is consistent with the Maxwell–Garnett formalism. Possible applications in determining the hybridization particle resonances of multi-shell structures and electromagnetic cloaking are identified. (paper)

On exact solutions for oscillatory flows in a generalized Burgers fluid with slip condition

Energy Technology Data Exchange (ETDEWEB)

Hayat, Tasawar [Dept. of Mathematics, Quaid-i-Azam Univ., Islamabad (Pakistan); Dept. of Mathematics, Coll. of Sciences, KS Univ., Riyadh (Saudi Arabia); Najam, Saher [Theoretical Plasma Physics Div., PINSTECH, P.O. Nilore, Islamabad (Pakistan); Sajid, Muhammad; Mesloub, Said [Dept. of Mathematics, Coll. of Sciences, KS Univ., Riyadh (Saudi Arabia); Ayub, Muhammad [Dept. of Mathematics, Quaid-i-Azam Univ., Islamabad (Pakistan)

2010-05-15

An analysis is performed for the slip effects on the exact solutions of flows in a generalized Burgers fluid. The flow modelling is based upon the magnetohydrodynamic (MHD) nature of the fluid and modified Darcy law in a porous space. Two illustrative examples of oscillatory flows are considered. The results obtained are compared with several limiting cases. It has been shown here that the derived results hold for all values of frequencies including the resonant frequency. (orig.)

Analysis of fast neutrons elastic moderator through exact solutions involving synthetic-kernels

International Nuclear Information System (INIS)

Moura Neto, C.; Chung, F.L.; Amorim, E.S.

1979-07-01

The computation difficulties in the transport equation solution applied to fast reactors can be reduced by the development of approximate models, assuming that the continuous moderation holds. Two approximations were studied. The first one was based on an expansion in Taylor's series (Fermi, Wigner, Greuling and Goertzel models), and the second involving the utilization of synthetic Kernels (Walti, Turinsky, Becker and Malaviya models). The flux obtained by the exact method is compared with the fluxes from the different models based on synthetic Kernels. It can be verified that the present study is realistic for energies smaller than the threshold for inelastic scattering, as well as in the resonance region. (Author) [pt

A two-dimensional method of manufactured solutions benchmark suite based on variations of Larsen's benchmark with escalating order of smoothness of the exact solution

International Nuclear Information System (INIS)

Schunert, Sebastian; Azmy, Yousry Y.

2011-01-01

The quantification of the discretization error associated with the spatial discretization of the Discrete Ordinate(DO) equations in multidimensional Cartesian geometries is the central problem in error estimation of spatial discretization schemes for transport theory as well as computer code verification. Traditionally ne mesh solutions are employed as reference, because analytical solutions only exist in the absence of scattering. This approach, however, is inadequate when the discretization error associated with the reference solution is not small compared to the discretization error associated with the mesh under scrutiny. Typically this situation occurs if the mesh of interest is only a couple of refinement levels away from the reference solution or if the order of accuracy of the numerical method (and hence the reference as well) is lower than expected. In this work we present a Method of Manufactured Solutions (MMS) benchmark suite with variable order of smoothness of the underlying exact solution for two-dimensional Cartesian geometries which provides analytical solutions aver- aged over arbitrary orthogonal meshes for scattering and non-scattering media. It should be emphasized that the developed MMS benchmark suite rst eliminates the aforementioned limitation of ne mesh reference solutions since it secures knowledge of the underlying true solution and second that it allows for an arbitrary order of smoothness of the underlying ex- act solution. The latter is of importance because even for smooth parameters and boundary conditions the DO equations can feature exact solution with limited smoothness. Moreover, the degree of smoothness is crucial for both the order of accuracy and the magnitude of the discretization error for any spatial discretization scheme. (author)

Modified method of simplest equation: Powerful tool for obtaining exact and approximate traveling-wave solutions of nonlinear PDEs

Science.gov (United States)

Vitanov, Nikolay K.

2011-03-01

We discuss the class of equations ∑i,j=0mAij(u){∂iu}/{∂ti}∂+∑k,l=0nBkl(u){∂ku}/{∂xk}∂=C(u) where Aij( u), Bkl( u) and C( u) are functions of u( x, t) as follows: (i) Aij, Bkl and C are polynomials of u; or (ii) Aij, Bkl and C can be reduced to polynomials of u by means of Taylor series for small values of u. For these two cases the above-mentioned class of equations consists of nonlinear PDEs with polynomial nonlinearities. We show that the modified method of simplest equation is powerful tool for obtaining exact traveling-wave solution of this class of equations. The balance equations for the sub-class of traveling-wave solutions of the investigated class of equations are obtained. We illustrate the method by obtaining exact traveling-wave solutions (i) of the Swift-Hohenberg equation and (ii) of the generalized Rayleigh equation for the cases when the extended tanh-equation or the equations of Bernoulli and Riccati are used as simplest equations.

Symbolic computation of exact solutions expressible in rational formal hyperbolic and elliptic functions for nonlinear partial differential equations

International Nuclear Information System (INIS)

Wang Qi; Chen Yong

2007-01-01

With the aid of symbolic computation, some algorithms are presented for the rational expansion methods, which lead to closed-form solutions of nonlinear partial differential equations (PDEs). The new algorithms are given to find exact rational formal polynomial solutions of PDEs in terms of Jacobi elliptic functions, solutions of the Riccati equation and solutions of the generalized Riccati equation. They can be implemented in symbolic computation system Maple. As applications of the methods, we choose some nonlinear PDEs to illustrate the methods. As a result, we not only can successfully obtain the solutions found by most existing Jacobi elliptic function methods and Tanh-methods, but also find other new and more general solutions at the same time

New exact travelling wave solutions of generalised sinh- Gordon and (2 + 1-dimensional ZK-BBM equations

Directory of Open Access Journals (Sweden)

Sachin Kumar

2012-10-01

Full Text Available Exact travelling wave solutions have been established for generalised sinh-Gordon andgeneralised (2+1 dimensional ZK-BBM equations by using GG      expansion method whereG  G( satisfies a second-order linear ordinary differential equation. The travelling wave solutionsare expressed by hyperbolic, trigonometric and rational functions.

Construction of exact solutions for the Stern-Gerlach effect

International Nuclear Information System (INIS)

Diaz Bulnes, J.; Oliveira, I.S.

2001-01-01

We obtain exact solutions for the Schroedinger-Pauli matrix equation for a neutral particle of spin 1/2 in a magnetic field with a field gradient. The analytical wave functions are written on the symmetry plane Y = 0, which contains the incident and splitted beams, in terms of the Airy functions. The time-evolution of the probability, |Ψ+| 2 and |Ψ-| 2 , and the eigenenergies are calculated. The include a small contribution from the field gradient, α, proportional to (α ℎ) 2/3 , which amount to equal energy displacements on both magnetic levels. The results are generalized for spin S = 3/2, and in this case we found that the m = ±1/2 and m = ±3/2 magnetic sublevels are unequally splitted by the field gradient, being the difference in energy of the order 0.4 MHz. Replacing real experimental parameters we obtained a spatial splitting of the spin up and spin down states of the order Δz ≅4 mm, in accordance to a real Stern-Gerlach experiment. (author)

Exact solitary wave solution for higher order nonlinear Schrodinger equation using He's variational iteration method

Science.gov (United States)

Rani, Monika; Bhatti, Harbax S.; Singh, Vikramjeet

2017-11-01

In optical communication, the behavior of the ultrashort pulses of optical solitons can be described through nonlinear Schrodinger equation. This partial differential equation is widely used to contemplate a number of physically important phenomena, including optical shock waves, laser and plasma physics, quantum mechanics, elastic media, etc. The exact analytical solution of (1+n)-dimensional higher order nonlinear Schrodinger equation by He's variational iteration method has been presented. Our proposed solutions are very helpful in studying the solitary wave phenomena and ensure rapid convergent series and avoid round off errors. Different examples with graphical representations have been given to justify the capability of the method.

Exact Solution of a Faraday's Law Problem that Includes a Nonlinear Term and Its Implication for Perturbation Theory.

Science.gov (United States)

Fulcher, Lewis P.

1979-01-01

Presents an exact solution to the nonlinear Faraday's law problem of a rod sliding on frictionless rails with resistance. Compares the results with perturbation calculations based on the methods of Poisson and Pincare and of Kryloff and Bogoliuboff. (Author/GA)

Exact Solutions of Fractional Burgers and Cahn-Hilliard Equations Using Extended Fractional Riccati Expansion Method

Directory of Open Access Journals (Sweden)

Wei Li

2014-01-01

Full Text Available Based on a general fractional Riccati equation and with Jumarie’s modified Riemann-Liouville derivative to an extended fractional Riccati expansion method for solving the time fractional Burgers equation and the space-time fractional Cahn-Hilliard equation, the exact solutions expressed by the hyperbolic functions and trigonometric functions are obtained. The obtained results show that the presented method is effective and appropriate for solving nonlinear fractional differential equations.

Exact Solution of the Gyration Radius of an Individual's Trajectory for a Simplified Human Regular Mobility Model

Science.gov (United States)

Yan, Xiao-Yong; Han, Xiao-Pu; Zhou, Tao; Wang, Bing-Hong

2011-12-01

We propose a simplified human regular mobility model to simulate an individual's daily travel with three sequential activities: commuting to workplace, going to do leisure activities and returning home. With the assumption that the individual has a constant travel speed and inferior limit of time at home and in work, we prove that the daily moving area of an individual is an ellipse, and finally obtain an exact solution of the gyration radius. The analytical solution captures the empirical observation well.

Generation of exact solutions to the Einstein field equations for homogeneous space--time

International Nuclear Information System (INIS)

Hiromoto, R.E.

1978-01-01

A formalism is presented capable of finding all homogeneous solutions of the Einstein field equations with an arbitrary energy-stress tensor. Briefly the method involves the classification of the four-dimensional Lie algebra over the reals into nine different broad classes, using only the Lorentz group. Normally the classification of Lie algebras means that one finds all essentially different solutions of the Jacobi identities, i.e., there exists no nonsingular linear transformation which transforms two sets of structure constants into the other. This approach is to utilize the geometrical considerations of the homogeneous spacetime and field equations to be solved. Since the set of orthonormal basis vectors is not only endowed with a Minkowskian metric, but also constitutes the vector space of our four-dimensional Lie algebras, the Lie algebras are classified against the Lorentz group restricts the linear group of transformations, denoting the essentially different Lie algebras, into nine different broad classes. The classification of the four-dimensional Lie algebras represents the unification of various methods previously introduced by others. Where their methods found only specific solutions to the Einstein field equations, systematic application of the nine different classes of Lie algebras guarantees the extraction of all solutions. Therefore, the methods of others were extended, and their foundations of formalism which goes beyond the present literature of exact homogeneous solutions to the Einstein field equations is built upon

General Exact Solution to the Problem of the Probability Density for Sums of Random Variables

Science.gov (United States)

Tribelsky, Michael I.

2002-07-01

The exact explicit expression for the probability density pN(x) for a sum of N random, arbitrary correlated summands is obtained. The expression is valid for any number N and any distribution of the random summands. Most attention is paid to application of the developed approach to the case of independent and identically distributed summands. The obtained results reproduce all known exact solutions valid for the, so called, stable distributions of the summands. It is also shown that if the distribution is not stable, the profile of pN(x) may be divided into three parts, namely a core (small x), a tail (large x), and a crossover from the core to the tail (moderate x). The quantitative description of all three parts as well as that for the entire profile is obtained. A number of particular examples are considered in detail.

Exact solution of the nucleons diffusion equation with increase inelastic cross section

International Nuclear Information System (INIS)

Portella, H.M.

1985-01-01

The successive aproximations method is applied to obtain an exact and compact analytical solution of the differential equation wich describes the diffusion of nucleonic component in the atmosphere, when the inelastic cross section of the air interaction nucleon-nucleus increases with the energy. The result is compared with the experimental data wich have been obtained in Chacaltaya (x=540g/cm 2 ) by the Brazil - Japan cooperation using emulsion chambers. The value of the constant a measurement of the variation of the cross section with the energy, that makes the best adjustment of the result found out with the experimental data is between 0.05 and 0.06. (M.C.K.) [pt

The zero mass limit of Kerr and Kerr-(anti-)de-Sitter space-times: exact solutions and wormholes

Science.gov (United States)

Birkandan, T.; Hortaçsu, M.

2018-03-01

Heun-type exact solutions emerge for both the radial and the angular equations for the case of a scalar particle coupled to the zero mass limit of both the Kerr and Kerr-(anti)de-Sitter spacetime. Since any type D metric has Heun-type solutions, it is interesting that this property is retained in the zero mass case. This work further refutes the claims that M going to zero limit of the Kerr metric is both locally and globally the same as the Minkowski metric.

Exact Solution of Gas Dynamics Equations Through Reduced Differential Transform and Sumudu Transform Linked with Pades Approximants

Science.gov (United States)

Rao, T. R. Ramesh

2018-04-01

In this paper, we study the analytical method based on reduced differential transform method coupled with sumudu transform through Pades approximants. The proposed method may be considered as alternative approach for finding exact solution of Gas dynamics equation in an effective manner. This method does not require any discretization, linearization and perturbation.

Exact solution for flow in a porous pipe with unsteady wall suction and/or injection

Science.gov (United States)

Tsangaris, S.; Kondaxakis, D.; Vlachakis, N. W.

2007-10-01

This paper presents an extension of the exact solution of the steady laminar axisymmetric flow in a straight pipe of circular cross section with porous wall, given by R.M. Terrill, to the case of unsteady wall injection and/or suction. The cases of the pulsating parabolic profile and of the developed pulsating flow are investigated as examples. The pulsating flow in porous ducts has many applications in biomedical engineering and in other engineering areas.

Exact Solutions of Fragmentation Equations with General Fragmentation Rates and Separable Particles Distribution Kernels

Directory of Open Access Journals (Sweden)

S. C. Oukouomi Noutchie

2014-01-01

Full Text Available We make use of Laplace transform techniques and the method of characteristics to solve fragmentation equations explicitly. Our result is a breakthrough in the analysis of pure fragmentation equations as this is the first instance where an exact solution is provided for the fragmentation evolution equation with general fragmentation rates. This paper is the key for resolving most of the open problems in fragmentation theory including “shattering” and the sudden appearance of infinitely many particles in some systems with initial finite particles number.

Heun Polynomials and Exact Solutions for the Massless Dirac Particle in the C-Metric

Science.gov (United States)

Kar, Priyasri; Singh, Ritesh K.; Dasgupta, Ananda; Panigrahi, Prasanta K.

2018-03-01

The equation of motion of a massless Dirac particle in the C-metric leads to the general Heun equation (GHE) for the radial and the polar variables. The GHE, under certain parametric conditions, is cast in terms of a new set of su(1, 1) generators involving differential operators of degrees ±1/2 and 0. Additional Heun polynomials are obtained using this new algebraic structure and are used to construct some exact solutions for the radial and the polar parts of the Dirac equation.

Exact solution for heat transfer free convection flow of Maxwell nanofluids with graphene nanoparticles

Science.gov (United States)

Aman, Sidra; Zuki Salleh, Mohd; Ismail, Zulkhibri; Khan, Ilyas

2017-09-01

This article focuses on the flow of Maxwell nanofluids with graphene nanoparticles over a vertical plate (static) with constant wall temperature. Possessing high thermal conductivity, engine oil is useful to be chosen as base fluid with free convection. The problem is modelled in terms of PDE’s with boundary conditions. Some suitable non-dimensional variables are interposed to transform the governing equations into dimensionless form. The generated equations are solved via Laplace transform technique. Exact solutions are evaluated for velocity and temperature. These solutions are significantly controlled by some parameters involved. Temperature rises with elevation in volume fraction while Velocity decreases with increment in volume fraction. A comparison with previous published results are established and discussed. Moreover, a detailed discussion is made for influence of volume fraction on the flow and heat profile.

The quasi-diffusive approximation in transport theory: Local solutions

International Nuclear Information System (INIS)

Celaschi, M.; Montagnini, B.

1995-01-01

The one velocity, plane geometry integral neutron transport equation is transformed into a system of two equations, one of them being the equation of continuity and the other a generalized Fick's law, in which the usual diffusion coefficient is replaced by a self-adjoint integral operator. As the kernel of this operator is very close to the Green function of a diffusion equation, an approximate inversion by means of a second order differential operator allows to transform these equations into a purely differential system which is shown to be equivalent, in the simplest case, to a diffusion-like equation. The method, the principles of which have been exposed in a previous paper, is here extended and applied to a variety of problems. If the inversion is properly performed, the quasi-diffusive solutions turn out to be quite accurate, even in the vicinity of the interface between different material regions, where elementary diffusion theory usually fails. 16 refs., 3 tabs

Exact Solutions for Two Equation Hierarchies

International Nuclear Information System (INIS)

Song-Lin, Zhao; Da-Jun, Zhang; Jie, Ji

2010-01-01

Bilinear forms and double-Wronskian solutions are given for two hierarchies, the (2+1)-dimensional breaking Ablowitz–Kaup–Newell–Segur (AKNS) hierarchy and the negative order AKNS hierarchy. According to some choices of the coefficient matrix in the Wronskian condition equation set, we obtain some kinds of solutions for these two hierarchies, such as solitons, Jordan block solutions, rational solutions, complexitons and mixed solutions. (general)

Exact solutions and conservation laws of the system of two-dimensional viscous Burgers equations

Science.gov (United States)

Abdulwahhab, Muhammad Alim

2016-10-01

Fluid turbulence is one of the phenomena that has been studied extensively for many decades. Due to its huge practical importance in fluid dynamics, various models have been developed to capture both the indispensable physical quality and the mathematical structure of turbulent fluid flow. Among the prominent equations used for gaining in-depth insight of fluid turbulence is the two-dimensional Burgers equations. Its solutions have been studied by researchers through various methods, most of which are numerical. Being a simplified form of the two-dimensional Navier-Stokes equations and its wide range of applicability in various fields of science and engineering, development of computationally efficient methods for the solution of the two-dimensional Burgers equations is still an active field of research. In this study, Lie symmetry method is used to perform detailed analysis on the system of two-dimensional Burgers equations. Optimal system of one-dimensional subalgebras up to conjugacy is derived and used to obtain distinct exact solutions. These solutions not only help in understanding the physical effects of the model problem but also, can serve as benchmarks for constructing algorithms and validation of numerical solutions of the system of Burgers equations under consideration at finite Reynolds numbers. Independent and nontrivial conserved vectors are also constructed.

Langevin synchronization in a time-dependent, harmonic basin: An exact solution in 1D

Science.gov (United States)

Cadilhe, A.; Voter, Arthur F.

2018-02-01

The trajectories of two particles undergoing Langevin dynamics while sharing a common noise sequence can merge into a single (master) trajectory. Here, we present an exact solution for a particle undergoing Langevin dynamics in a harmonic, time-dependent potential, thus extending the idea of synchronization to nonequilibrium systems. We calculate the synchronization level, i.e., the mismatch between two trajectories sharing a common noise sequence, in the underdamped, critically damped, and overdamped regimes. Finally, we provide asymptotic expansions in various limiting cases and compare to the time independent case.

Integrals of the motion and exact solutions of the problem of two dispersing delta-wells

International Nuclear Information System (INIS)

Man'ko, V.I.; Chikhachev, A.S.

1998-01-01

An exact solution is analyzed for the analogs of bound and scattering states in a nonstationary quantum mechanical system whose potential has the form of two dispersing delta-wells. For the delta-potentials explicit (in the form of operator kernels) expressions are found for the integrals of the motion that depend on time and transform to the known integrals of the motion for a free quantum particle as the interaction force with the potential approaches zero

Exact models for isotropic matter

Science.gov (United States)

Thirukkanesh, S.; Maharaj, S. D.

2006-04-01

We study the Einstein-Maxwell system of equations in spherically symmetric gravitational fields for static interior spacetimes. The condition for pressure isotropy is reduced to a recurrence equation with variable, rational coefficients. We demonstrate that this difference equation can be solved in general using mathematical induction. Consequently, we can find an explicit exact solution to the Einstein-Maxwell field equations. The metric functions, energy density, pressure and the electric field intensity can be found explicitly. Our result contains models found previously, including the neutron star model of Durgapal and Bannerji. By placing restrictions on parameters arising in the general series, we show that the series terminate and there exist two linearly independent solutions. Consequently, it is possible to find exact solutions in terms of elementary functions, namely polynomials and algebraic functions.

Realization of Quasi-Omnidirectional Solar Cells with Superior Electrical Performance by All-Solution-Processed Si Nanopyramids.

Science.gov (United States)

Zhong, Sihua; Wang, Wenjie; Tan, Miao; Zhuang, Yufeng; Shen, Wenzhong

2017-11-01

Large-scale (156 mm × 156 mm) quasi-omnidirectional solar cells are successfully realized and featured by keeping high cell performance over broad incident angles (θ), via employing Si nanopyramids (SiNPs) as surface texture. SiNPs are produced by the proposed metal-assisted alkaline etching method, which is an all-solution-processed method and highly simple together with cost-effective. Interestingly, compared to the conventional Si micropyramids (SiMPs)-textured solar cells, the SiNPs-textured solar cells possess lower carrier recombination and thus superior electrical performances, showing notable distinctions from other Si nanostructures-textured solar cells. Furthermore, SiNPs-textured solar cells have very little drop of quantum efficiency with increasing θ, demonstrating the quasi-omnidirectional characteristic. As an overall result, both the SiNPs-textured homojunction and heterojunction solar cells possess higher daily electric energy production with a maximum relative enhancement approaching 2.5%, when compared to their SiMPs-textured counterparts. The quasi-omnidirectional solar cell opens a new opportunity for photovoltaics to produce more electric energy with a low cost.